Question 280683: Mary rides up a slope on a ski lift at 120 feet per minute. She skis down at 2640 feet per minute. the round trip took 20 minutes. How long is the ski lift?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! We have to assume the distances are the same, despite our knowledge that skiers go back and forth across the mountain while the ski lift goes straight up/down, but with vertical "droops".
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Distance equation is: d=rt
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120 fpm = speed of the lift
2460 fpm = speed of the skier
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roundtrip time = 20 min
x = time spent on the lift
20 -x = skiing time
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The distance covered at each speed is equal (by assumption), so the lift r*t = skier r*t.
d = 120x
d = 2,640(20-x)
d = d, so
120x = 2640(20-x)
120x = 52,800 - 2,640x
2,760x = 52,800
x = 19.13 min riding the lift
which means
20-x = .87 min skiing
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120*19.13 = lift distance = 2295.6 ft
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2,295.6/2,640 = .86954545 or about .87
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So that checks.
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Answer:
The ski lift is 2295.6 ft in length.
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Done.
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P.S.
Skiing @ 2640 fpm means 1/2 mile/minute * 60 min/hr = 30 mph. Fast, but not incredible.
Riding a ski lift @ 120 fpm means 1.4 mph, which is incredibly slow. 20 mph is more realistic.
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