Question 1083541
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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.
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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

{{{160/r + 160/(r+8)}}} = 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.


<U>Check</U>.  {{{160/32 + 160/40}}} = 5 + 4 = 9 hours.
</pre>

The solution by "josgarithmetic" is WRONG.