SOLUTION: A bicyclist rode up a mountain road at 12 km/h and then back down at 30 km/h. If the round trip toook 3.5 hours, how long did the ride up the mountain take?

Algebra ->  Length-and-distance -> SOLUTION: A bicyclist rode up a mountain road at 12 km/h and then back down at 30 km/h. If the round trip toook 3.5 hours, how long did the ride up the mountain take?      Log On


   

Question 166790: A bicyclist rode up a mountain road at 12 km/h and then back down at 30 km/h. If the round trip toook 3.5 hours, how long did the ride up the mountain take?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
A bicyclist rode up a mountain road at 12 km/h and then back down at 30 km/h. If the round trip toook 3.5 hours, how long did the ride up the mountain take?

Remember: Speed=Distance%2Ftime, EQN 1
Given---S%5Bup%5D=12kph,S%5Bdn%5D=30kph;time=3.5hrs
*Note: time=t%5Bup%5D%2Bt%5Bdn%5D, EQN 2
Via EQN 1, we get --> Distance=Speed%2Atime
Since both distance is the same, we equate both going up and down:
D%5Bup%5D=D%5Bdn%5D
S%5Bup%5D%2At%5Bup%5D=S%5Bdn%5D%2At%5Bdn%5D, EQN 3
Via EQN 2, we get t%5Bdn%5D=time-t%5Bup%5D, EQN 4 ---> subst. in EQN 3:
S%5Bup%5D%2At%5Bup%5D=S%5Bdn%5D%2A%28time-t%5Bup%5D%29
%2812%29%2At%5Bup%5D=%2830%29%283.5-t%5Bup%5D%29
12%2At%5Bup%5D=105-30t%5Bup%5D
12t%5Bup%5D%2B30t%5Bup%5D=105
42t%5Bup%5D=105 ------> cross%2842%29t%5Bup%5D%2Fcross%2842%29=cross%28105%292.5%2Fcross%2842%29
highlight%28t%5Bup%5D=2.5hrs%29, ANSWER in going up
For the record, Via EQN 2---> t%5Bdn%5D=3.5-2.5=1hr, going down
* This just make sense, that it will take more time to go up than to go down.
Check Via EQN 3:
12%2A2.5=30%2A1
30km=30km
Thank you,
Jojo