Question 1083541: Paige drives her motorcycle 160 miles to her friend's house. It starts to rain, so Paige borrows her friend's car for the return trip along the same route. She averages 8mph faster on the motorcycle than in the car. If her total time for both parts of her trip, without rest stops or other traffic delays, is 9 hours, find Paige's average speed while driving the car.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website!
"faster on the motorcycle than in the car"
SPEED TIME DISTANCE
MOTORCYCLE r+8 160/(r+8) 160
CAR r 160/r 160
Total 9
Solve this time sum equation for r:
(corrected)
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
Paige drives her motorcycle 160 miles to her friend's house. It starts to rain, so Paige borrows her friend's car for the return trip
along the same route. She averages 8mph faster on the motorcycle than in the car. If her total time for both parts of her trip,
without rest stops or other traffic delays, is 9 hours, find Paige's average speed while driving the car.
~~~~~~~~~~~~~~~~~
Let "r" be Paige averaged speed on the car, in miles per hour..
Then her averaged speed on the motorcycle is (r+8) mph, according to the condition.
Therefore, your "time equation" is
 = 9.
Simplify and solve it. Your first step is to multiply both sides by r*(r+8) to rid of denominators.
I solved it mentally: averaged speed by car is 32 mph, averaged speed by the motorcycle is 40 mph.
But you solve it step by step to learn on how to do it.
Check.  = 5 + 4 = 9 hours.
The solution by "josgarithmetic" is WRONG.
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