SOLUTION: A plane which can fly 100 miles an hour in still air can fly 500 miles with a wind which is blowing at a certain rate in 5/8 of the time it would require to fly 500 miles against a

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Question 149374: A plane which can fly 100 miles an hour in still air can fly 500 miles with a wind which is blowing at a certain rate in 5/8 of the time it would require to fly 500 miles against a wind blowing at the same rate. What was the rate of the wind?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A plane which can fly 100 miles an hour in still air can fly 500 miles with a wind which is blowing at a certain rate in 5/8 of the time it would require to fly 500 miles against a wind blowing at the same rate. What was the rate of the wind?
:
Let x = the rate of the wind
then
(100-x) = speed against the wind
and
(100+x) = speed with the wind
:
Write a time equation: Time = dist%2Fspeed
:
With the wind time = Against time * 5%2F8
500%2F%28%28100%2Bx%29%29 = 500%2F%28%28100-x%29%29 * 5%2F8
500%2F%28%28100%2Bx%29%29 = 2500%2F%288%28100-x%29%29
500%2F%28%28100%2Bx%29%29 = 2500%2F%28%28800-8x%29%29
Cross multiply:
2500(100+x) = 500(800-8x)
:
250000 + 2500x = 400000 - 4000x
;
2500x + 4000x = 400000 - 250000
:
6500x = 150000
x = 150000%2F6500
x = 23.1 mph, the rate of the wind
:
:
Check solution, find the time for each trip
500%2F123.1 = 4.06 hrs
500%2F76.9 * 5%2F8 = 4.06 hr