<PRE><B>Question 195887</B>
An airplane travels 500 miles against the wind in 5 hours and makes the return
 trip with the same wind in 2 hours. Find the rate of the wind.
:
Let w = the rate of the wind
Let s = speed of the plane in still air
:
Write a distance equation for each trip
5(s-w) = 500; against the wind
2(s+w) = 500; with the wind
:
Simplify, divide the 1st equation by 5, the 2nd equation by 2:
s - w = 100
s + w = 250
---------------addition eliminates w, find s
2s = 350
s = {{{350/2}}}
s = 175 mph, speed of the plane
:
Use s + w = 250, to find w
175 + w = 250
w = 250 - 175
w = 75 mph is the wind
:
:
Check solution in the 1st equation
5(s - w) = 500
5(175 - 75) = 500
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