Question 202100
a ski lift carries a skier up a slope at the rate of 800 feet per minute and
 he returns from the top to the bottom on a path parallel to the lift at an
 average rate of 2640 feet per minute.
How long is the lift if the round trip traveling time is 20 minutes?
:
Let d = the length of the lift
:
Write a time equation: Time = {{{dist/speed}}}
:
Time up + time down = 20 min
{{{d/800}}} + {{{d/2640}}} = 20
Multiply equation by 211200:
211200*{{{d/800}}} + 21120*{{{d/2640}}} = 211200*20
Cancel out the denominators:
264d + 80d = 4224000
:
344d = 4224000
d = {{{4224000/344}}}
d = 12,279.07 feet
:
:
Check solution using this value in the time equation:
{{{12279.07/800}}} + {{{12279.07/2640}}} = 
15.349 + 4.651 = 20.00