Questions on Word Problems: Travel and Distance answered by real tutors!

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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?: 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(4189) About Me  (Show Source):
You can put this solution on YOUR website!
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/speed
:
With the wind time = Against time * 5/8
500/((100+x)) = 500/((100-x)) * 5/8
500/((100+x)) = 2500/(8(100-x))
500/((100+x)) = 2500/((800-8x))
Cross multiply:
2500(100+x) = 500(800-8x)
:
250000 + 2500x = 400000 - 4000x
;
2500x + 4000x = 400000 - 250000
:
6500x = 150000
x = 150000/6500
x = 23.1 mph, the rate of the wind
:
:
Check solution, find the time for each trip
500/123.1 = 4.06 hrs
500/76.9 * 5/8 = 4.06 hr