SOLUTION: A ski lift carried Maria up a slope at a rate of 6 km/h, and she skied back down parallel to the lift at 34 km/h. The round trip took 30 min. How far did she ski and for how long?

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Question 794251: A ski lift carried Maria up a slope at a rate of 6 km/h, and she skied back down parallel to the lift at 34 km/h. The round trip took 30 min. How far did she ski and for how long?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A ski lift carried Maria up a slope at a rate of 6 km/h, and she skied back down parallel to the lift at 34 km/h.
The round trip took 30 min.
How far did she ski and for how long?
:
Change 30 min to .5 hrs
:
Let d = distance up and distance down
:
Write a time equation, time = dist/speed
time up + time down = .5 hrs
d%2F6 + d%2F34 = .5
Multiply by the least common multiple: 102
102*d%2F6 + 102*d%2F34 = 102(.5)
Cancel the denominators
17d + 3d = 51
20d = 51
d = 51/20
d = 2.55 km she skied
:
Find her time down the hill
2.55/34 = .075 hrs which is: .075(60) = 4.5 minutes
:
:
Check this by finding the time up:
2.55/6 = .425 hrs
.425 + .075 = .5 Which is 30 min