Algebra 2
Applications of Rational Equations
Name:
Period:
Worksheet #2:
1) Walking Speed Marcie can walk 8 miles in the same time as Frank walks 6 miles. If Marcie walks 1 mile
per hour faster than Frank, then how fast does each person walk?
Solution: Let x = Frank’s walking speed. Then x+1 = Marcie’s walking speed.
Time for Frank: 𝑇 =
6
𝑇
Time for Marcie: 𝑇 =
8
𝑇+1
Use the given time relationship to write an equation relating Frank and Marcie.
Find the LCD and solve the equation:
Solving this gives x = 3 so 3 mph is Frank’s speed and 4 mph is Marcie’s speed.
2) Kiyoshi can paint a certain fence in 3 hours by himself. If Red helps, the job takes only 2 hours. How long
would it take Red to paint the fence by himself?
Kiyoshi’s rate:
Total Work =
Red’s rate:
𝑇𝑇𝑇
ℎ𝑇𝑇𝑇𝑇
=
because we don’t know Red’s rate (x)
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2
Total Work = Kiyoshi’s Work + Red’s Work. Substitute the above expressions and solve.
Together, it takes them 1.6 hours.
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3) Joe and John are planning to paint a house together. John thinks that if he worked alone, it would take him
3 times as long as it would take Joe to paint the entire house. Working together, they can complete the job in
24 hours. How long would it take each of them, working alone, to complete the job?
Use their combined rates to write an equation that is equal to one job.
It would take Joe 32 hours and John 96 hours to complete the job on their own.
4) Edgar can blow the leaves off the sidewalks around the capitol building in 2 hours using a gasolinepowered blower. Ellen can do the same job in 8 hours using a broom. How long would it take them working
together?
Together, it takes them 1.6 hours.
5) Melissa walks 3 miles to the house of a friend and returns home on a bike. She averages 4 miles per hour
faster when cycling than when walking, and the total time for both trips is two hours. Find her walking speed.
Melissa’s walking speed is 2 miles per hour.
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6) If two inlet pipes can fill a pool in one hour and 30 minutes, and one pipe can fill the pool in two hours and
30 minutes on its own, how long would the other pipe take to fill the pool on its own? On its own, the other pipe would take 3.75, or 3 hours and 75 minutes.
7) Mari and Liam can each wash a car and vacuum its interior in 2 hours. Zach needs 3 hours to do this same
job alone. If Zach, Liam, and Mari work together, how long will it take them to clean a car?
Together, they can clean the car in 45 minutes.
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