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Chapter 6.5: Applications of Rational
Equations
Objectives: Set up and solve work problems Set up and solve motion problems Distance =(Rate)x(Time)
Steps for Solving Application Problems:
- Read, understand the question
- Assign a variable (What is it asking for?)
- Write an equation
- Solve the equation
- Check, does it make sense?
Work Formula:
(timetakestogether) 1 job timetakes2ndperson/thing
1 (timetakestogether) timetakes1stperson/thing
1
Solving For Time It Takes To Do a Task Together
Ex: One person can do a task in 6 hours. Another can do the same task in 4 hours. How long will it take them to do the task together?
Let ______ = __________________________
Equation:
1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job
_____________ __________ _____________ __________ _______
Answer: They can do the task together in 2.4 hours.
Solving For Time It Takes a Person/Thing To Do a Task Alone
Ex: Say you and a friend can do a task in 12 hours. You can do the same task by yourself in 18 hours. How long would it take your friend to do the task alone?
Let ______ = __________________________
Equation:
1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job
_____________ __________ _____________ __________ _______
Answer: It would take your friend 36 hours to do the task alone.
Solving Problems Involving Negative Work
Ex: Say a pipe can fill a tank in 4 hours, and another pipe can empty the tank in 6 hours. If both pipes are working, how long will it take to fill the tank?
Let ______ = __________________________
Equation:
1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job
_____________ __________ _____________ __________ _______
Answer: It takes 12 hours to fill the tank while both pipes are working.
Ex: While one pipe is pumping water in and another is pumping water out, a tank can be filled 75 minutes. If the pipe that pumps water out was only working, the tank could be emptied in 50 minutes. If the pipe that pumps water in was only working, how long would it take to fill the tank?
Let ______ = __________________________
Equation:
1 over timeit takes1stperson/thing timeit takestogether 1 over timeit takes2ndperson/thing timeit takestogether 1 job
_____________ __________ _____________ __________ _______
Answer: It would take 30 minutes to fill the tank if the pipe that pumps water in was only working.
Ex: Say a dude rides a bike on a trail part of the time at 6 mph and part of the time at 10 mph. If the total distance traveled was 28 miles in 4 hours, how long did the dude ride at each speed?
Let ______ = __________________________ Then _________ = _____________________________
Rate Distance rate
dist time
1 st^ Part of the trail
2 nd^ Part of the trail
total
Equation:
timeit tookfor the1stpart timeit tookfor the2ndpart totaltimeit took
_____________ _____________ __________ ___
Answer: The dude rode 6 mph for 3 hours, and 10 mph for 1hour.
Ex: Say you and a friend started off on a trail at the same time, but you went 9 mph, and your friend went 6 mph. Since you went faster, you finished the trail 0.25 hours before your friend. Determine the length of the trail.
Let ______ = __________________________
Rate Distance rate
dist time
You
Your friend
Equation:
Answer: The trail is 4.5 miles long.
