In yesterday s lesson we learned how to solve rational equations and check for extraneous solutions.

Transcription

1 NAME: DATE: Algebra 2: Lesson 9-4 Rational Equation Word Problems Learning Goals: 1) How do we setup and solve word problems involving rational equations? In yesterday s lesson we learned how to solve rational equations and check for extraneous solutions. In today s lesson we are going to talk about rational equations and their applications to the real world. We will focus on two different types of word problems. Word problems involving work Word problems involving motion. When solving word problems, it is always a good idea to define the variable you are solving for! Word Problems Involving Work When problems involve two people working together on a job then their rates add and they can perform the job working together in a shorter amount of time. the time taken by the first person to complete the job the time taken by the second person to complete the job the time it takes for them working together to complete the job If we let x = time it takes 1 person to complete the task, then his work rate is 1. In other words, he x can complete the 1 job in x number of hours. Example: Bill s garden hose can fill the pool in 10 hours. His neighbor has a hose than can fill the pool in 15 hours. How long will it take to fill the pool using both hoses? Equation needed in order to solve this problem: = 1 x 1. Joe can complete his yard work in 3 hours. If his son helps it will take only 2 hours working together. How long would the yard work take if his son is working alone?

2 2. Tom can paint a small house in 5 hours. Huck can paint a small house in 4 hours. On Saturday, they have to paint 3 small houses. Working together, how long will it take them to paint the 3 houses? 3. Norm and Cliff can paint a room in 5 hours working together. Being a professional painter, Norm can paint twice as fast as Cliff. How long would it take Cliff to paint a room by himself?

3 Word Problems Involving Motion When objects are in motion, a variation of the distance formula must be used. distance = rate time This formula can be manipulated in order to change it to a formula that will give a rational expression for the time. This variation is Distance divided by Rate equals Time. Example: Adam drives 15 mph faster than David does. Adam can drive 100 miles in the same amount of time that David drives 80 miles. Find Adams driving speed. Table used to help setup equation: Distance Rate Time David 80 x 80 x Adam 100 x x + 15 Equation needed in order to solve this problem: 80 x = 100 x A passenger train can travel 20mph faster than a freight train. If the passenger train can cover 390 miles in the same time it takes the freight train to cover 270 miles, how fast is each train?

4 5. The first leg of Mary s road trip consisted of 120 miles of traffic. When the traffic cleared she was able to drive twice as fast for 300 miles. If the total trip took 9 hours how long was she stuck in traffic? 6. Gilbert took 2 hours longer to drive 240 miles on the first day of a business trip than to drive 144 miles on the second day. If his rate was the same both days, what was his driving time for each day?

5 Objects Moving With or Against (Wind or Current) When an object is moving with or against wind/current, it can speed up or slow down the rate. Moving with the wind or current (downstream) will speed up the rate of the object. Moving against the wind or current (upstream) will slow down the rate of the object. 7. Jon is kayaking a river which flows downstream at a rate of 1 mile per hour. He paddles 5 miles downstream and then turns around and paddles 6 miles upstream. The trip takes 3 hours. How fast can Jon paddle in still water? 8. A plane flies 910 miles with the wind in the same time it can go 660 miles against the wind. The speed of the plan in still air is 305 miles per hour. What is the speed of the wind?