Question 280683
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".
.
Distance equation is:  d=rt
.
120 fpm = speed of the lift
2460 fpm = speed of the skier
.
roundtrip time = 20 min
x = time spent on the lift
20 -x = skiing time
.
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
.
120*19.13 = lift distance = 2295.6 ft
.
2,295.6/2,640 = .86954545 or about .87
.
So that checks.
.
Answer:
The ski lift is 2295.6 ft in length.
.
Done.
.
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.