SOLUTION: Tina rides her bike 15m up a hill and then 15m. down the same hill. This complete trip takes 2 hours. If her downhill speed is 20m faster than her uphill speed, how fast does she

Question 354442: Tina rides her bike 15m up a hill and then 15m. down the same hill. This complete trip takes 2 hours. If her downhill speed is 20m faster than her uphill speed, how fast does she ride uphill?
I have these variables and have tried them every which way but loose...
uphill- distance=15, rate=r, and time=t ;
downhill- distance=15, rate=r+20, and time=2-t
No matter what I do, nothing looks workable for me...I think my brain is stuck.
Thank you, BP
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Tina rides her bike 15m up a hill and then 15m. down the same hill. This complete trip takes 2 hours. If her downhill speed is 20m faster than her uphill speed, how fast does she ride uphill?
---------
I'll assume you mean 20 km/hr faster, and that the distances are km, not meters.
----------
d = rt (r = uphill rate)
t = d/r
2 hr = 15/r + 15/(r+20)
2*r*(r+20) = 15(r+20) + 15r
2r^2 + 40r = 15r+300 + 15r
2r^2 + 10r - 300 = 0
r^2 + 5r - 150 = 0
(r + 15)(r - 10) = 0
r = 10 km/hr uphill, 30 km/hr downhill

RELATED QUESTIONS
Really stumped on this one!!! A bike is rode 15 miles up a hill and then 15 miles back (answered by josmiceli)

a girl rides her bike up a hill at 10 miles per hour. She then rides her bike down the... (answered by robertb)

Nancy can ride her bike uphill at eight kilometers per hour, and downhill at twelve... (answered by josmiceli)

Mary can x-country ski down a hill 6 km / hour faster than she can ski up the hill. If it (answered by josgarithmetic,Alan3354)

A bicyclist rides his bicycle 20 miles up a hill and then comes back down. His speed... (answered by jorel1380)

A bicyclist rides his bicycle 12 miles up a hill and then comes back down. His speed... (answered by ikleyn)

Mary rides her bike to john's house, she returns the same way. She rides at a constant... (answered by solver91311)

If Charlene biked up a hill at a speed of 12 miles per hour and came down the hill using... (answered by Alan3354)

A biker rode up a 20-km hill in 2 hours and down the hill in .5 hour without stopping .... (answered by Alan3354)