SOLUTION: Evan hiked up a mountain at 3km/h and returned at 4km/h. The entire trip took 5 hours and 10 minutes, including the half hour he spent at the top.How long was the trail?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Evan hiked up a mountain at 3km/h and returned at 4km/h. The entire trip took 5 hours and 10 minutes, including the half hour he spent at the top.How long was the trail?      Log On


   

Question 274956: Evan hiked up a mountain at 3km/h and returned at 4km/h. The entire trip took 5 hours and 10 minutes, including the half hour he spent at the top.How long was the trail?
Found 3 solutions by josmiceli, ankor@dixie-net.com, checkley77:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write a separate equation for each part of the trip
going up:
d%5Bu%5D+=+r%5Bu%5D%2At%5Bu%5D
going down:
d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D
--------------
given:
Distance is the same for both trips: call it d
r%5Bu%5D+=+3+ km/hr
r%5Bd%5D+=+4 km/hr
I only want Evan's time hiking, 5 hrs 10 min minus 30 min =
4 hrs 40 min = 4.667 hrs
t%5Bu%5D+%2B+t%5Bd%5D+=4.667 hr
-------------------
substituting:
d+=+3%2A%284.667+-+t%5Bd%5D%29
d+=+4t%5Bd%5D
3%2A%284.667+-+t%5Bd%5D%29+=+4t%5Bd%5D%29
14+-+3t%5Bd%5D+=+4t%5Bd%5D
7t%5Bd%5D+=+14
t%5Bd%5D+=+2 hrs
and,since
t%5Bu%5D+%2B+t%5Bd%5D+=4.667
t%5Bu%5D+=+4.667+-+2
t%5Bu%5D+=+2.667 hrs
The length of the trail is d
d+=+4t%5Bd%5D
d+=+4%2A2
d+=+8
The trail is 8 km long

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Evan hiked up a mountain at 3km/h and returned at 4km/h.
The entire trip took 5 hours and 10 minutes, including the half hour he spent at the top.
How long was the trail?
:
We are only interested in his hiking time 5:10 - :30 = 4:40 min
4 + 40/60 = 42%2F3 hrs or 14%2F3 hrs
:
Let d = one way dist:
:
write a time equation: Time = dist/speed
:
Up time + down time = total time
d%2F3 + d%2F4 = 14%2F3
Multiply equation by 12, results:
4d + 3d = 4(14)
7d = 56
d = 56%2F7
d = 8 miles one way
:
:
Check solution by finding the times
8/3 + 8/4 =
2.67 + 2 = 4.67 which is 42%2F3 hrs

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT
D=3X UP THE MOUNTAIN
D=4(14/3-X)
3X=56/3-4X
3X+4X=56/3
7X=56/3
X=(56/3)/7
X=56/3*1/7
X=56/21
X=8/3
X=2 HOURS 40 MIN TO CLIMB UP THE MOUNTAIN.
D=3*8/3
D=8 MILES UP THE MOUNTAIN.
PROOF:
8=4(14/3-8/3)
8=4(6/3)
8=4*28=8