SOLUTION: Boris hiked up a mountain trail and camped overnight at the top. The next day he returned down the same trail. His average rate traveling uphill was 2.4 kilometers per hour and his

Question 366734: Boris hiked up a mountain trail and camped overnight at the top. The next day he returned down the same trail. His average rate traveling uphill was 2.4 kilometers per hour and his average rate downhill was 3.6 kilometers per hour. If he spent a total of 11 hours hiking, how long was the trail?
Found 2 solutions by mananth, solver91311:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
up mountain
let distance be x km
speed = 2.4
time = x/2.4
..
down the mountain
speed = 3.6 km/h
time = x/3.6
...
x/2.4 +x/3.6 = 11
(3.6x+2.4x)/3.6*2.4=11
6x= 11*3.6*2.4
/6
x=11*3.6*2.4 /6
x=15.84 km .....
...
m.ananth@hotmail.ca
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the distance either up or down the hill (we presume that the hill neither grew nor shrank overnight). Let represent the time to cover the distance going uphill at . Then the time for the downhill trip must have been

Recalling that , describe the uphill trip:

which can be written:

Next, describe the downhill trip:

and then solve for :

Set the two expressions equal to each other:

Cross-multiply, collect like terms, and solve for

John

My calculator said it, I believe it, that settles it

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