APPLICATIONS Judo Math Inc.

Transcription

1 APPLICATIONS 2013 Judo Math Inc.

2 8th Grade Black Belt Training: Problem Solving Discipline Order of Mastery - Applications (EE.7, SP.3) 1. Converting Units 2. Rate of Change 3. D=RT 4. Distance/Time graphs Okuden (secret teachings) 5. Mixtures 6. Work Rate You were originally taught how to convert units in elementary school. By converting, I mean change miles to meters or minutes to hours. You probably forgot all the conversions, which is not a big deal because you can always look those up. But once you look them up, do you remember if you have to multiply or divide? That s the real problem! What operation do you do once you have the conversion? WARNING: WHAT I M ABOUT TO TELL YOU IN THIS BELT WILL WORK FOR EVERY CONVERSION YOU EVER DO FOR THE REST OF YOUR LIFE. IT S THAT HUGE! That s what this belt is about. Applying your problem solving skills to the everyday world around us. This is where math meets Physics. Motion, speed, and velocity get involved. This is the stuff you ll use in high school and beyond. Good luck grasshopper! Standards Included: 8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height Judo Math Inc.

3 1. Converting Units Before we try to convert rates, we need to sharpen some basic converting skills first. So remember this: Whenever you need to convert something.anything: MULTIPLY BY THE CONVERSION. That s right. You re always multiplying.by the conversion Example: Convert 35 miles into kilometers So you looked up the conversion and you saw that 1 mile = 1.6 km (actually a good one to remember) Any conversion can be written as a fraction: 1 mile = 1.6km 1mile 1.6km or 1.6km 1mile So now I just need to MULTIPLY BY THE CONVERSION. But which one do I multiply? miles miles It helps to know that WORDS cancel out just like numbers do in a fraction: 1 If you have a MILES on top of a fraction, it ll cancel out with a MILES on the bottom If we use the first conversion: 35miles 1 1mile 1.6km = 35milesmiles 1.6km or miles 2 22 km Does that make sense? No!!!!! What we NEED is km on TOP because that s what it said to convert to 35miles 1.6km 1 1mile 35miles 1.6km 1 1mile ( 35)(1.6) km 1 = 56 km miles cancel out Left with only km It s tempting for some of you to avoid this process and simply try to memorize whether to multiply or divide. That s the single most popular mistake people make when converting. They think they know.but they don t. So try this conversion. 1. You are stuck on an island that has no currency; instead it uses the following exchange rate: o 50 bananas = 20 coconuts o 30 coconuts = 12 fish o 100 fish = 1 hammock You would like to buy a boat to get off this island. A boat will cost 10,000 bananas. You make hammocks. How many hammocks will you need to purchase a boat? 1

4 Metric conversions are quite simple. Why aren t we using the metric system? 1 Kilometer (km) = 1000 Meters 1 Kilogram (kg) = 1000 Grams 1 Kiloliter = 1000 liters 1 Meter = 100 Centimeters (cm) 1 Gram = 100 Centigrams 1 Liter = 100 centiliters 1 Meter = 1000 Millimeters (mm) 1 Gram = 1000 Milligrams 1 Liter = 1000 milliliters Notice a pattern??? Convert the following: 1) 3.4 liters to milliliters 6) 45 meters to centimeters 2) 876 millimeters to meters 7) 11.7 grams to kilograms 3) 78,999 milligrams to grams 8) kiloliters to centiliters 4) centigrams to micrograms 9) 444 centimeters to meters 5) 112 kilometers to millimeters 10) 277,000,000 centibytes to Megabytes Still feel like skipping out on writing it down? Try this very unique conversion: ET (a cute and friendly alien) wants to go home to his home planet, Brodo Asogi. He is designing a ship that will take him there. Brodo Asogi is approximately 12 million miles away from Earth. ET can build a ship that can fly 250,000 miles per day - that's pretty fast. E.T. needs to convert from Earth units to Brodo Asogi units, the information he needs is in the table below: 1 day =.05 bobos (a bobo is a day on Brodo Asogi) 100 miles = 1 putputs (a putput is like a mile on Brodo Asogi) How many days will it take E.T. to get home? How many bobos will it take ET to get home? How far away (in putputs) is Brodo Asogi from earth? How fast (in putputs per bobo) can ET s ship fly? 2

5 2. Rate of Change When you say you're driving 55 mph that is a rate of change. 55 miles for every one hour. It's an important distinction that you must understand to truly calculate speed. Try these. 1. A hot air balloon rose from a height of 100 m to 400 m in 3 minutes. What was the balloon s rate of change? 2. A glacier advanced down a mountain from an elevation of 2010 m to 1780 m in 5 years. What was the glaciers rate of change? 3. A sky diver falls 100 meters in 10 seconds. Calculate the rate of change. Hint: He starts at 0 when he jumps out of the plane. 4. A missile flies 20 miles in 10 minutes. Calculate the missile s rate of change. 5. A student s grade goes from a 95 to a 60 in 3 weeks because they didn t do their homework (this can happen to all of you in this class right now if you slack off!) Calculate the student s rate of grade change. 6. A patient s systolic blood pressure drops from 210 mm/hg to 100 mm/hg in 10 minutes after they took nitroglycerin. Calculate the patient s rate of change in blood pressure. 3

6 Converting rates is just like converting units.just harder. But not to worry because you still remember my advice! Whenever you need to convert: JUST MULTIPLY BY THE CONVERSION! Good to know conversions 1 mile = 5280 feet 1 meter = 3.3 feet 1 hour = 3600 seconds 1 mile = 1.6 kilometers 1 yard = 3 feet Example: Your mom was driving her minivan at a very safe speed of 30 miles/hr. How fast was she going in ft/sec? Since I know I m multiplying by a conversion I m going to start by writing what I have on the left as a fraction. Don t forget to include the UNITS, the physical words of miles and hrs. VERY IMPORTANT! WHAT I NEED 30miles 1hr feet sec Now I m going to write what I NEED way over on the right side of my paper, to keep things in order. So I need to end up with feet/sec.with feet on TOP and seconds on the BOTTOM. That will help me figure out where things go when I multiply. Let s start on the top. I have miles and I NEED to get to feet. The conversion for miles to feet is: 1 mile = 5280 feet Since I need feet on top, I m going to multiply by that conversion with the feet on TOP. That way the miles cancel out. 30miles 1hr 5280ft 1mile = 158,400 feet 1hr Now I ve got feet/hr, but I need feet/sec so.. I keep on going! Now I can convert the BOTTOM. I need to convert hours into seconds: 1hr = 3600 secs Since I NEED seconds on the bottom when I m done.i ll put the seconds on the bottom in the conversion. Now the hours cancel out: feet 1hr ft 1hr 3600sec 3600sec 44 ft/sec 4

7 How Fast Will My Egg Go? I m sure you ve all heard of the famous Egg Drop project. You need to build a device that will protect an egg when dropped from a certain distance. Say you dropped your device from 30 feet. You obviously wanted to make it go as slow as possible to avoid going splat. So you took a stopwatch and timed how long it took to hit the ground. So you ve got the Distance, and you ve got a Time. Now you want to find out how fast it went. That s called the Rate. Fortunately, we ve got a formula for that, where Distance equals the Rate multiplied by the Time DISTANCE = RATE x TIME or d = r t 30 ft = r (2.43) 30 feet r = feet/sec 2.43 secs But how fast was that in miles per hour? We ll have to convert it! Like we did before! feet/sec is like saying feet 1 second To convert this, we multiply.getting rid of the unwanted units like feet and seconds: There are 5,280 feet in one mile and there are 3600 seconds in an hour. Let s start by converting the seconds to hours: Then convert the feet to miles: feet x 3600 seconds = feet x 1 mile = mile = 8.4 miles/hour 1 second 1 hour 1 hour 5280 feet 5280 hour Now you give it a shot. Complete the table: DISTANCE (miles) RATE (miles/hour) TIME (hours) , Take the following rates, given in miles per hour, and convert them into feet per second. (YOU MUST SHOW YOUR WORK TO GET CREDIT, LIKE THE EXAMPLES ABOVE) MILES PER HOUR FEET PER SECOND

8 Now take these totals that are in feet per second, and change them to miles per hour FEET PER SECOND MILES PER HOUR Alex is a fast-talker. He speaks at a pace of 240 words per minute. What s his pace in words per second? 13. Michael went on a skateboarding trip across the country. He knew it would be tiresome pushing his skateboard the whole way, so he paced himself, going just 9.17 feet per second. What was his speed in miles per hour? 14. Your egg drop project was so well designed, you tried dropping it from the 75 foot building across the street, and it worked! When you timed it, you saw that it took seconds to reach the ground. a. How fast did your egg project go in feet per second? b. How fast did it go in miles per hour? c. What about kilometers per hour? d. Meters per second? e. What do you think is the best unit to measure your drop in? Explain why. 6

9 3. Messing with D=RT DISTANCE = RATE X TIME Sounds easy enough. If you were driving at a rate of 60 mph and you drove for 3 hours, you d just multiply the two together and you d find that you drove a distance of 180 miles. But the reason it s easy is because all the units line up. What if they didn t? Sometimes you need to convert first before you use the formula. CONVERT..THEN DERT (get it? The E means equals) Example: Mr. T. drove at a rate of 65 miles/hour for a total of 20 minutes. How far did he travel in miles? To figure this out, let s create a vertical chart to show our data. Distance:? miles Rate: miles 60 hour Time: 20 minutes See how these two match? miles=miles But these two don t! hours minutes So we need to convert minutes into hours so they all match up. Now the problem can be solved. 20 minutes 1 hour = Time in hours 60 minutes 20 minutes 1 hour = 60 minutes 20 1 hour = 60 1 hour = 3 Distance = Rate Time = 60 miles 1 hour 1 hour 3 = 60 miles 1 hour 1 hour 3 = 60 miles 3 = 20 miles 7

10 Now you try: 1. If a car is traveling at 30 miles per hour, how many minutes will it take for it to travel 10 miles? D: R: T: 2. If a car travels 100 miles in 4 hours, how fast is it traveling in kilometers per hour? D: R: T: 3. Anthony sees Jordan 1/4 of a mile away. Jordan is riding her bicycle towards Anthony at two miles per hour. How much time, in minutes, will it take Jordan to reach Anthony? D: R: T: 4. Hannah drove to Justin's house at 53 mph. Justin's house is twenty-five miles away. What time did she arrive at Justin's house, if she left at 2:14 p.m.? D: R: T: 5. Alyssa drove to the beach, which is one hundred thirteen kilometers away, at fifty-two kph. She drove home the next day at sixty-two kph. How many hours in total did Alyssa spend driving? D: R: T: 8

11 6. James drove to Hailey's house at 60 mph. Hailey's house is fifty miles away. James arrived at Hailey's house at 4:10 p.m. What time did he leave? D: R: T: 7. Taylor drove to the mall, which is eleven kilometers away. She left at 2:57 and arrived at the mall at 3:12. What was her average driving speed in miles per hour? D: R: T: 8. Victoria and Jonathan both live eighteen miles from school. If Victoria drives to school at thirty-six mph and Jonathan drives to school at fifty mph, how many more minutes will it take Victoria to get to school? D: R: T: 9. Last year, Amanda's speed in a bike race was 5 kph. She finished in 6 hours and 12 minutes. What must be Amanda's average speed (in kph) if she is to finish in 3 hours and 6 minutes this year? D: R: T: 10. Kenny and Michael dropped their cupid s arrow project from the roof, and when it hit the ground, it sent pieces of wood flying everywhere. Just 3 seconds after it hit the ground, the wing flew 12 meters across the courtyard, striking Mr. Ray in the head. How fast was the wing going, in miles per hour? D: R: T: 9

12 DRT practice 1) Mr. T decided to build a super fast balloon car to beat Mr. Gallagher. Mr. T's car careened through the hallway in ½ of a second. The tracks was two meters long. How fats was the car going? (meters/sec, feet/sec, miles/hr) 2) Billy Bob Thornton, the potbelly pig, drove from his house to the Farmer's Market (which is 2 miles away) at 5:31 in the morning. He drove at the average speed of 20 miles/hour. He stayed at the market eating pies for two hours. He drove home at the average speed of 2 miles/hour, because he was so full. What time did he get home? 3.) Convert 7.5 meters/sec to miles/hour, km/hour, and feet/second. 4.) The zoingo boingo egg drop device dropped from HTHMA (30 feet) at an average of 2 miles/hour. How long did it take for the device to hit the ground? 5.) Pinky Winky went to the mall. The drive to the mall is 3 miles. He drove at a speed of 15 miles/hour there and back. He stayed at the mall for two hours. How long was the trip in total? 6) Mr. T ran out of tic-tacs and since he is addicted to them, he ran from his house to 7-11 at 15 miles/hour and it's 50 miles from his house. How long did it take him to get to 7-11 in minutes? 7) Tod drove his car to the mall. He left his house at 2:30 and got to the mall at 3:15. The mall is 108 miles from his house. How fast was he going in miles/hour and meters/sec? 8) Tod and Bob are in a car race. The distance they have to go is 55 miles. It took Tod 15 minutes to the reach the end, it took Bob 25 minutes. How fast were each of them going in miles/hour? What was the difference between Tod and Bob's speeds? 9) The Chargers were neck and neck with the Patriots, 14 to 12. The Chargers had the ball, Rivers threw the ball but then the guy that looked like he was on steriods caught the ball and ran forty yards in 10 seconds. How fast was he going in yards per minute? 10) Martha was in a race and ran a 55 mile course in 50 minutes. How fast was she going in miles/hour? 11) If Emma's balloon car moved at 3 feet/sec. How fast was it going in meters/sec, km/hr, miles/hr? 12) Maya sees Skylar 15 miles away, Skylar is driving her car at.75 mph. How long will it take for her to reach Maya? 13) If Bob leaves the house at 3:35 pm for the store, he drove at 35 mph. The store was 70 miles away. He stayed there for two hours, then drove home at 20 mph. When did he arrive back home? 14) Emma was driving to the mall, and she got there at 2:30 pm. She had been driving at at 20 mph and the mall was 15 miles away. When did she leave home? 15) Willie had just eaten a bag of candy and was really hyper. He decided to go to the store to buy more candy, the store was 10 miles away. He ran there at 19 mph. How long did it take him? 10

13 ENOUGH WITH THE DIRT ALREADY! 1. Light travels at a speed of 187,000 miles per second, and the Sun is about 93 million miles away from the earth.(remember? That s called 1 AU) How many minutes does it take light to reach the Earth from the Sun? How fast does light travel in miles per hour? 2. Luis broke the rules, and went to 7-11 after school at 3:45. Since he was going to get in trouble if he was caught, he ran the whole way there. He got to 7-11 at 3:51. If it s only 1 mile to the store, how fast was Luis running in miles per hour? What about in feet per second? 3. Hunter and Jake both live fourteen miles from school. If Hunter drives to school at thirty mph and Jake drives to school at fifty-nine mph, how many more minutes will it take Hunter to get to school? How many more seconds? 4. Daniel made the world s best Egg Drop Device. He was so confident, he dropped it off the top of Rock Church. It only took 1.5 seconds to crash on the ground. Since he s a genius with gravity, he calculated that it was going 14.7 meters per second. With that info, how tall is Rock church in feet? How fast was Daniel s device going in miles per hour? 5. Langston s bag of Hamster bedding worked perfectly. When he dropped it from 30 feet, it survived without a scratch, even though it only took.56 seconds to reach the ground. How fast was it going in miles per hour? What about meters per second? 11

14 6. Lawrence is the fastest man alive. He ran 40 meters in 4.3 seconds. What was his velocity in feet per second? In miles per hour? 7. Arielle went to buy milk at the store. Albertson s was a 2 mile walk from her house. It took her 15 minutes to walk there. How fast did she walk in miles per hour? In kilometers per hour? 8. Faith needed to buy Adobe Photoshop at the computer store. She rode her bike at a speed of 23 miles per hour to get there. It took her just ten minutes to get there. How far away, in feet, was the computer store? What about in miles? 9. Ronnie pulled off the world s most amazing skateboarding trick. He s now in the Guiness Book of World Records for the longest stair ride. He was really haulin, going 12 meters per second down the stairs. His historic ride lasted 8 seconds. How long, in feet, was this monumental staircase? What was his speed in miles per hour? 10. Molly threw the football a monstrous 115 feet. It went across the grass field and hit Faith right in the eye. While she was crying, Naomi was playing around with a radar gun and saw that the ball went 25 meters per second. How long did it take from the time Molly threw it to the time it hit Faith, in seconds? In minutes? 12

15 4. Distance/Time Graphs Look at the Distance/Time graph on the following sheet. It represents a race between Solid Stevens and Dashed Davis. (Get it? Solid versus dashed? I know I m lame) Answer the following questions about the race. 1. If this race was 30 feet long, who won the race, solid or dashed? 2. If this race was 20 feet long, who won? 3. Where was solid located 14 seconds into the race? 4. Did either runner ever stop? 5. Did either runner ever turn around? 6. At what distance(s) in the race were both runners tied? 7. What was solid s average speed? What was dash s average speed? 8. How fast was solid running between 0 and 13 feet? 9. How fast was dash running between 0 and 13 feet? 10. How fast was solid running between 28 and 34 seconds? 11. At what intervals were they running at a constant speed? 12. What does the steepness of the line tell you about the runner? 13. How far ahead was solid after 8 seconds? 14. What was each runner s average speed between 28 and 52 seconds? Describe what the race would look like between those 24 seconds

16 The Great Race!!!

17 The Great Assessment of The Great Race Look at the Distance/Time graph on the back of this sheet. It represents a race between three different runners. Answer the following questions about the race. 1. Who won this race? 2. If this race was only 20 feet long, who would ve won? 3. If this race was only 10 feet long, who would ve won? 4. Did either runner ever stop? 5. Did either runner ever go backwards? 6. At what distance(s) in the race were all three runners tied? 7. What was the average speed of runner A? 8. What was the average speed of runner B? 9. Who ran the fastest at any one given interval? 10. What does the steepness of the line tell you about the runner? 11. How fast was runner B going in the first 10 feet? 12. How fast was runner A going between 25 and 28 seconds? 13. How fast was runner C going between 20 and 27 seconds? 14. Was runner B in the lead at any point in this race? 15. How far ahead was runner A from the other two runners, 17 seconds into the race? 14

18 The Great Race!!! A B C

19 CONVERTING RATES REVIEW Let s practice that popular formula! Complete the table: DISTANCE (miles) RATE (miles/hour) TIME (hours) The following two rates are given in miles/hr. Convert them into feet per second The next two rates are given in feet per second. Convert them into miles/hr The next two are given in meters/second. Convert them into miles/hr Brad went on a skateboarding trip across the country. He knew it would be tiresome pushing his skateboard the whole way, so he paced himself, going just feet per second. What was his speed in miles per hour? 13. Your egg drop project was so well designed, you tried dropping it from the 100 foot building across the street, and it worked! When you timed it, you saw that it took seconds to reach the ground. a. How fast did your egg project go in feet per second? b. Meters per second? 14. Jessie and Victoria both live 10 miles from school. If Jessie drives to school at 25 mph and Victoria drives to school at 60 mph, how many more minutes will it take Jessie to get to school? THE FOLLOWING RATES ARE IN FEET PER SECOND. CONVERT THEM INTO: met/sec, mph, km/hr

20 Mixing it up A popular problem in Algebra is called a mixture problem. It involves mixing two things together, like chemical solutions or nuts, then figuring out what the mixture looks like afterwards. The basic formula looks like this: (% of 1 st )(Amount of 1 st ) + (% of 2 nd )(Amount of 2 nd ) = (% total)(amount of total) Example: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution? Basically, it s saying 20% of something + 50% of 40 equals 30% of both of them. That s where Algebra and that formula above can help out. We don t know how many liters of the first solution, so we ll call that X Let s start plugging in what we ve got: (20%)x + (50%)(40) = 30%(total) But what should we put as the total? If I add x amount plus 40, I get x So we can put that in: (20%)x + (50%)(40) = 30%(x +40) Since you are a Fundamentals Black Belt you know that in order to multiply percents I need to make them into a decimal..2x +.5(40) =.3(x + 40) Now I can solve for x!.2x + 20 =.3x x -.2x 20 =.1x =.1x x = 80 So you need 80 liters of 20% solution

21 Try these on for size 1) 9 m³ of soil containing 30% sand was mixed into 3 m³ of soil containing 50% sand. What is the sand content of the mixture? 2) An acid solution was made by mixing 4 qt. of a 25% acid solution and 2 qt. of a 10% acid solution. What is the concentration of the mixture? 3) For his birthday party John mixed together 7 gal. of Brand A fruit punch and 2 gal. of Brand B. Brand A contains 54% fruit juice and Brand B contains 36% fruit juice. What percent of the mixture is fruit juice? 4) A metal alloy weighing 6 kg and containing 50% gold is melted and mixed with 9 kg of pure gold. What percent of the resulting alloy is gold? 5) What is the price per oz of bleached flour if 16 oz were mixed with 8 oz of unbleached flour which costs $8/oz to make 24 oz of baking flour which costs $4/oz? 6) 3 ml of a sugar solution was mixed with 12 ml of pure water to make a 8% sugar solution. Find the percent concentration of the first solution. 7) 8 fl. oz. of an acid solution was mixed with 12 fl. oz. of pure water to make a 6% acid solution. Find the percent concentration of the first solution. 8) Scott made a nut mixture that contains 41% peanuts by mixing together 19 oz. of mixed nuts that contain 30% peanuts and 11 oz. of a different brand of mixed nuts. The second brand of mixed nuts contained what percent peanuts? 9) How many oz. of a metal containing 78% iron must be combined with 2 oz. of pure iron to form an alloy containing 82% iron? 10) How many kg of copper which costs $3/kg must be added to 1 kg of tin which costs $8/kg to make bronze which costs $4/kg? 11) How many oz of soybean oil which costs $3/oz must be added to 11 oz of canola oil which costs $1/oz to make vegetable oil which costs $2/oz? 12) How many ml of a 55% alcohol solution must be mixed with 1 ml of a 15% alcohol solution to make a 35% solution? 13) Ashley wants to make a 16% saline solution. She has already poured 11 qt. of a 20% saline solution into a beaker. How many qt. of a 5% saline solution must she add to this to create the desired mixture? 14) 6 L of an acid solution was mixed with 2 L of a 34% acid solution to make a 49% acid solution. Find the percent concentration of the first solution. 15) How much of Brand A fruit punch (10% fruit juice) must be mixed with 5 gal. of Brand B fruit punch (55% fruit juice) to create a mixture containing 25% fruit juice? 16) How much soil with 44% clay do you need to add to 8 ft³ of soil with 20% clay in order to make a soil with 28% clay? 17

22 Work Rate Finish Faster Another popular problem is called a Work problem. In other words, if it takes me 2 hours to mow the lawn, and it takes my daughter 5 hours to mow the lawn, how long would it take if both of us did it together? We re working.hence the name. The reason it s a little strange is because the time it takes will be less if we work together. Of course there s a trick to this if you think logically. Think of it as one JOB in ONE hour. If it takes me 2 hours to do the job then I can do 2 1 of the JOB in 1 hour. If it takes my daughter 5 hours to do the job then she can do 1 of the JOB in 1 hour. We can then add those together to figure out what part we could 5 both do in one hour That means together we can do 10 7 of the job in one hour. So how long will it take us both together? Let s call that x. That means we can do x 1 of the job in one hour. 1 7 So.. x 10 Our ratio mastery tells us x = 10 7 = 1.4 hrs But in real life would you ever say 1.4 hours? No! we d use hours and minutes. If there was just some way I could CONVERT the.4 hours into minutes Oh yeah! 60 minutes = 1 hour so I MULTIPLY BY THE CONVERSION.4hrs 1 60min 1hr 24 minutes So together my daughter and I can mow the lawn in 1 hr and 24 minutes 18

23 How long can it take? 1) Working alone, it takes Matt 14 hours to harvest a field. Wilbur can harvest the same field in 9 hours. How long would it take them if they worked together? 3) Ted can mop a warehouse in 8 hours. Julio can mop the same warehouse in 11 hours. Find how long it would take them if they worked together. 5) Working alone, it takes Maria nine hours to pick forty bushels of apples. Stefan can pick the same amount in 12 hours. How long would it take them if they worked together? 7) Working together, Matt and Scott can tar a roof in 6.96 hours. Had he done it alone it would have taken Scott 15 hours. How long would it take Matt to do it alone? 9) Working together, Kristin and Darryl can pick forty bushels of apples in 6.16 hours. Had he done it alone it would have taken Darryl 14 hours. How long would it take Kristin to do it alone? 11) Molly can pick forty bushels of apples in 10 hours. Chelsea can pick the same amount in 14 hours. How long would it take them if they worked together? 13) Working alone, Stephanie can harvest a field in 10 hours. Kayla can harvest the same field in 16 hours. If they worked together how long would it take them? 15) Working together, Asanji and Imani can harvest a field in 5.24 hours. Had she done it alone it would have taken Imani 11 hours. Find how long it would take Asanji to do it alone. 2) Working alone, Micaela can dig a 10 ft by 10 ft hole in ten hours. Krystal can dig the same hole in nine hours. Find how long it would take them if they worked together. 4) Ndiba can mop a warehouse in 8 hours. Amy can mop the same warehouse in 12 hours. If they worked together how long would it take them? 6) Working alone, it takes Nicole 13 hours to pick forty bushels of apples. Ming can pick the same amount in 9 hours. Find how long it would take them if they worked together. 8) Working together, Adam and Mofor can inflate twenty balloons in 7.47 minutes. Had he done it alone it would have taken Mofor 14 minutes. Find how long it would take Adam to do it alone. 10) Working together, Lisa and Brenda can pick forty bushels of apples in 7.24 hours. Had she done it alone it would have taken Brenda 14 hours. Find how long it would take Lisa to do it alone. 12) Working together, Rob and Totsakan can clean an attic in 5.45 hours. Had he done it alone it would have taken Totsakan 12 hours. Find how long it would take Rob to do it alone. 14) Rob can install a new deck in 12 hours. Pranav can install the same deck in 14 hours. If they worked together how long would it take them? 16) Working together, Willie and Kristin can wash a car in 6.35 minutes. Had she done it alone it would have taken Kristin 15 minutes. Find how long it would take Willie to do it alone. 19

24 ANSWERS TO PROBLEM SOLVING BLACK BELT APPLICATIONS CONVERTING UNITS Intro Banana problem: 16 hammocks 1) ).876 3) 79 4) 56 5) 112,000,000 6) ) ) 90 9) ) 277 ET problem: 48 days 2.4 bobos 120,000 putputs 50,000 putputs/bobo RATE OF CHANGE meters/min meters/year meters/sec 4. 2 miles/min points/week 6. 11mm/hg/min HOW FAST WILL MY EGG GO? a) 4.24 b) 2.88 c) 4.6 d) 1.28 MESSING WITH DIRT minutes kilometers/hr 3. 7 and a half minutes 4. it takes 29 minutes, so 2: hrs 6. it takes 50 minutes, so left at 3: mph 8. 8 minutes kph mph DRT PRACTICE 1. 4 meters/sec, 13.2 ft/sec, 9 miles/hr 2. 8:37 am miles/hr, 27 km/hr, ft/sec second 5. 2 hours 24 minutes minutes mph, 64 meters/sec 8. Todd 220 miles/hr, Bob 132 miles/hr, Difference of 88 mph yards/minute miles/hr miles/hr, 3.3 km/hr,.9 meters/sec hrs :05 pm 14. 1:45 pm minutes ENOUGH WITH DIRT ALREADY! million miles/hr 8.3 minutes miles/hr 14.7 ft/sec minutes 854 seconds feet 33 miles/hr meters/sec 36.5 miles/hr fps 20.9 mph 7. 8 mph 12.8 kph 8. 20,240 feet 3.83 miles mph feet sec.023 min DISTANCE/TIME GRAPHS GREAT RACE ANSWERS 1. solid 2. dashed yes 5. dashed and and all 12. how fast feet ahead of dash 14. solid.71 dash varies CONVERTING RATES REVIEW , , 12.27, , 22.5, 36 MIXING IT UP 1. 35% 2. 20% 3. 50% 4. 80% 5. $ % 7. 15% 8. 60% 9. 9oz 10. 4kg oz 12. 1ml 13. 4qt % gall 16. 4cuft WORK RATE