SOLUTION: Tina hiked 15 km up a mountain trail. Her return trip along the same trail took 1/2 hour less, because she increased her speed by 1 km/hr. How long did it take her to climb up an

Click here to see ALL problems on Travel Word Problems

Question 557241: Tina hiked 15 km up a mountain trail. Her return trip along the same trail took 1/2 hour less, because she increased her speed by 1 km/hr. How long did it take her to climb up and down the trail?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Tina hiked 15 km up a mountain trail.
Her return trip along the same trail took 1/2 hour less, because she increased her speed by 1 km/hr.
How long did it take her to climb up and down the trail?
:
Let t = time down the trail
then
(t+.5) = up the trail
:
Write a speed equation: Speed = dist/time
:
speed down - speed up = 1 km/h
- = 1
Multiply eq by t(t+.5), results:
15(t+.5) - 15t = t(t+.5)
15t + 7.5 - 15t = t^2 + .5t
A quadratic equation from this
0 = t^2 + .5t - 7.5
You can use the quadratic formula but this will factor
(t-2.5)(t+3) = 0
:
t = 2.5 hrs; is the time down the hill
then
2.5 + .5 = 3 hr; is the time up the hill
;
Check this by finding the speeds:
15/2.5 = 6 km/h down the hill
15/3 = 5 km/h up the hill