# Jeremy Gregory held the 3,000 yard swim record for 13 year-old males in He swam 3,000 yards in 30 minutes.

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1 Rate Conversions Lesson 1.5 Jeremy Gregory held the 3,000 yard swim record for 13 year-old males in He swam 3,000 yards in 30 minutes yards Jeremy found his rate of speed in yards per minute. 30 minutes = 100 yards 1 minute He swam 100 yards per minute. 30 Jeremy s coach wanted to know Jeremy s speed in feet per minute. Changing units on rates is called a rate conversion. Jeremy s coach did a rate conversion to change 100 yards per minute to feet per minute. Find the conversion factor relating yards and feet. 1 yard = 3 feet rate. 1 yard 3 feet or 3 feet 1 yard Multiply the original rate by one of the rates above. One of the rates can be used to cancel out the unwanted unit of measurement. Below, notice the rate in green allows yards to be canceled. The remaining answer is in feet per minute. The yellow rate does not work since both yards and feet remain in the final rate. 100 yards 1 minute 1 yard = _ 100 yard yard OR yards feet 3 minute feet 1 minute 3 feet = _ 300 yard feet = 300 feet 1 yard 1 minute yard 1 minute The original rate of 100 yards per minute had the yards unit in the numerator. Canceling out yards requires the conversion rate to have yards in the denominator. 22 Lesson 1.5 ~ Rate Conversions

2 Example 1 Convert 48 miles per hour to miles per minute. Write the rate as a fraction. Write the conversion factor that relates hours to minutes. conversion rate. Choose the conversion rate with hours in the numerator since hours is in the denominator of the original rate. 48 miles = 60 minutes 60 minutes or 60 minutes Multiply the original rate and the conversion rate. Cancel units. Simplify the rate to a unit rate. Forty-eight miles per hour is equal to 0.8 miles per minute. 48 miles = 48 miles 60 minutes 60 minutes 48 miles = 0.8 miles 60 minutes 1 minute Sometimes the units in both the numerator and the denominator need to be converted to find the unit rate. If this is the case, pick one unit of measurement to convert first. Complete that conversion. Then, perform the second conversion on the new rate. Example 2 Rolando rides his scooter 9 kilometers per hour. Find his rate in meters per minute. Write the rate as a fraction. Choose one unit of measurement to convert first. Write the conversion factor that relates hours to minutes. conversion rate. Choose the conversion rate with hours in the numerator since hours is in the denominator of the original rate. 9 kilometers = 60 minutes 60 minutes or 60 minutes Multiply the original rate and the conversion rate. Cancel units. 9 kilometers 60 minutes = 9 kilometers 60 minutes Lesson 1.5 ~ Rate Conversions 23

3 Example 2 (Continued) Write the conversion factor that relates kilometers to meters. conversion with kilometers in the denominator since kilometers is in the numerator of the original rate. 1 kilometer = 1,000 meters 1000 meters or 1 kilometer 1 kilometer 1000 meters Multiply the rate from the first conversion and the conversion rate. Cancel units. 9 kilometers 1000 meters = 9000 meters 60 minutes 1 kilometer 60 minutes Simplify the rate to a unit rate meters = 150 meters 60 minutes 1 minute Rolando traveled 150 meters per minute on his scooter. exercises 1. Which of the following rates are equal to 1? Write all of the rates that apply. 1 foot 12 inches 1 meter yard centimeters 4 feet 60 minutes 1 mile 5000 feet 2000 pounds 1 ton Complete each rate so it is equal to kilometer meters 3. 1 gallon quarts 4. seconds 5. 1 mile inches 6. _ centimeters inches 1 kilometer 7. 1 yard Convert each rate to feet per hour miles per hour miles per hour feet per minute 24 Lesson 1.5 ~ Rate Conversions

4 Determine which rate should be used to complete each of the following conversions miles to feet hour A. 1 mile 5280 feet or B feet 1 mile 3 meters to meters 1 minute second A. 1 minute 60 seconds or B. 60 seconds 1 minute gallons per hour to gallons per second A. _ 3600 seconds or B. _ 3600 seconds 1 pound pounds per box to ounces per box A. 16 ounces or B. 16 ounces 1 pound 15. A dog barks 20 times in 10 minutes. a. Write this as a unit rate in barks per minute. b. Convert the rate to barks per hour. 16. A snail travels at a rate of inches per minute. Find this rate in inches per second. 17. Inessa walks 5 miles per hour. Find Inessa s rate in feet per second. 18. Michael was rock climbing El Capitan in Yosemite National Park. He climbed up the rock wall at a rate of 0.1 feet per second. Find Michael s climbing rate in feet per hour. 19. The average respiratory rate of an adult is 12 breaths per minute. What is an adult s average number of breaths per day? 20. A parachutist falls at a rate of 18 feet per second. Find the rate of fall in miles per hour. 21. Nate s heart beats about 103,680 times per day. How many times does his heart beat per minute? 22. Quincy drinks 70 ounces of water per day. How many ounces of water will she drink in one year? 23. Ted drove 180 miles in 3 hours. Shanda drove 35 miles in 30 minutes. Assume each person drove at a constant rate. Which person drove faster? Use mathematics to justify your answer. 24. Jerry stirred 2 tablespoons of lemonade mix into 4 quarts of water. Kandice stirred 6 tablespoons of lemonade mix into 12 quarts of water. Write the directions that should be on the lemonade mix explaining the rate of tablespoons of mix to use to quarts of water. Lesson 1.5 ~ Rate Conversions 25

5 review Write a ratio for each situation in simplest form. 25. Thirty-five students out of 100 interviewed prefer snow to sunshine. a. Write the ratio of students who prefer snow to the total students interviewed. b. Write the ratio of students who prefer sunshine to the total students interviewed. c. Write the ratio of students who prefer snow to those who prefer sunshine. 26. Sixteen boys and 24 girls signed up for the class field trip. a. Write the ratio of boys to girls who signed up for the class field trip. b. Write the ratio of boys to total students who signed up for the class field trip. c. Write the ratio of girls to total students who signed up for the class field trip. Write each rate as a unit rate. \$ hours miles 1.5 hours 29. Rodney measured the length of his room. It was 14 1_ 2 feet long. Write the length of his room as a decimal. 30. Watson measured the height of his locker. It was 72.4 centimeters tall. Write the height of his locker as a mixed number in simplest form. Tic-Tac-Toe ~ How Fast? In the United States, the speed limit on most freeways is 55 miles per hour. In Europe, however, speed would be written as kilometers per hour. Some conversions from customary units to metric units are given below. 1 inch 2.54 centimeters 1 foot centimeters 1 mile 1.61 kilometers Convert each speed to a metric speed. Round to the nearest hundredth if necessary miles per hour to kilometers per hour miles per hour to kilometers per hour miles per hour to meters per hour miles per hour to centimeters per hour feet per minute to centimeters per minute 6. 1,000 feet per minute to centimeters per second miles per hour to kilometers per minute inches per second to meters per hour 26 Lesson 1.5 ~ Rate Conversions

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