SOLUTION: a man ride a ski lift at the rate of 5 miles per hour and skis back down the hill at the rate of 50 miles an hour. If the complete trip requires 22minutes, how far is it from the b

Algebra ->  Human-and-algebraic-language -> SOLUTION: a man ride a ski lift at the rate of 5 miles per hour and skis back down the hill at the rate of 50 miles an hour. If the complete trip requires 22minutes, how far is it from the b      Log On


   

Question 606625: a man ride a ski lift at the rate of 5 miles per hour and skis back down the hill at the rate of 50 miles an hour. If the complete trip requires 22minutes, how far is it from the bottom to the top of the hill?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
a man ride a ski lift at the rate of 5 miles per hour and skis back down the hill at the rate of 50 miles an hour. If the complete trip requires 22minutes, how far is it from the bottom to the top of the hill?
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Let d = the distance from the bottom to the top of the hill
The round trip takes 22 minutes = 22/60 hours
The total time = the time uphill + the time downhill
t = 22/60 = d/5 + d/50
Solve for d:
22/60 = 10d/50 + d/50 = 11d/50
1/30 = d/50
d = 50/30 = 1 2/3 mi = 1.667 mi
Check:
Total trip = 22/60 = (5/3)/5 + (5/3)/50 = 1/3 + 1/30 = 11/30 = 22/60