SOLUTION: Please help me solve this word problem, thanks: A backpacker walks 2 miles uphill and 5 miles downhill in 3 hours. The same trip in the opposite direction takes 4 hours. Find the p

Question 712964: Please help me solve this word problem, thanks: A backpacker walks 2 miles uphill and 5 miles downhill in 3 hours. The same trip in the opposite direction takes 4 hours. Find the person's rate uphill and downhill.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A backpacker walks 2 miles uphill and 5 miles downhill in 3 hours.
The same trip in the opposite direction takes 4 hours.
Find the person's rate uphill and downhill.
:
let x = speed uphill
let y = speed down hill
:
Write a time equation for each way; time = dist/speed
+ = 3
multiply by xy, get rid of the denominators
2y + 5x = 3xy
and
+ = 4
multiply by xy
5y + 2x = 4xy
:
using elimination, mult the 1st eq by 4, the 2nd eq by 3
8y + 20x = 12xy
15y + 6x = 12xy
---------------------subtraction eliminates xy
-7y + 14x = 0
14x = 7y
divide both sides by 7
2x = y
:
In the 1st original equation replace y with 2x
+ = 3
multiply by 2s
2(2) + 5 = 2x(3)
4 + 5 = 6x
9 = 6x
x = 9/6
x = 1.5 mph up hill
:
we know y = 2x, therefore
y = 3 mph down hill
:
Check this in the 2nd original equation
5/1.5 + 2/3 =
3.33 + .67 = 4 hrs
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