SOLUTION: A cyclist bikes at a constant speed for 24 miles. He then returns home at the same speed but takes a different route. His return trip takes 1 hour longer and is 29 miles. Find h

Question 31099: A cyclist bikes at a constant speed for 24 miles. He then returns home at the same speed but takes a different route. His return trip takes 1 hour longer and is 29 miles. Find his speed.
I had this problem on a test and got it wrong. I now know the answer is 5, but I still don't understand HOW to get the answer. I really want to learn how to do this. I would appreciate any help. Thanks.
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
This question seems unsensable because it doesn't have a consant in its equation:
Let the speed be x
Going speed = x and returning speed = x
Equation:

29(x)-24(x)=(x)(x)





Solve by comlpleting the square:



Simpplify:



You get x=5

Or you can factor the left side:

You get x(x-5)=0

x=0 or x=5

Hence, the speed going and reutrning is 5mph.

Paul. 

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