SOLUTION: tina hiked 15 km up a mountain trail. Her return trip along the same trail took 30 minutes less because she was able to increase her speed by 1km/hour . how long did it take her

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Question 258762: tina hiked 15 km up a mountain trail. Her return trip along the same trail took 30 minutes less because she was able to increase her speed by 1km/hour . how long did it take her to climb up and down the mountain ?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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tina hiked 15 km up a mountain trail.
Her return trip along the same trail took 30 minutes less because she was able to increase her speed by 1km/hour.
how long did it take her to climb up and down the mountain?
:
Change 30 min to .5 hrs
:
Find the hiking rate first, then find the time:
:
Let r = T's rate up the mt
then
(r+1) = time down the mt
:
Write a time equation; time = dist/speed
:
Time up the mt - time down the mt = .5 hrs
15%2Fr - 15%2F%28r%2B1%29 = .5
multiply equation by r(r+1), results
15(r+1) - 15r = .5r(r+1)
:
15r + 15 - 15r = .5r^2 + .5r
Arrange as a quadratic equation
.5r^2 + .5r - 15 = 0
Multiply by 2, get rid of the decimals
r^2 + r - 30 = 0
Factor
(r+6)(r-5) = 0
the positive solution is what we want here
r = 5 km/hr hiking rate up the mt
:
Find the time up:
15/5 = 3 hrs
find the time down
15/6 = 2.5 hrs, (a difference of 30 min)