SOLUTION: A plane has a cruising speed of 150 miles per hour when there is no wind. At this speed, a plane flew 300 miles with the wind in the same amount of time it flew 200 miles against t

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Question 922036: A plane has a cruising speed of 150 miles per hour when there is no wind. At this speed, a plane flew 300 miles with the wind in the same amount of time it flew 200 miles against the wind. Find the speed of the wind.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
With a wind speed of x miles per hour,
a plane with a cruising speed of 150 miles per hour
travels with the wind at a speed of 150%2Bx miles per hour with respect to the ground,
while against the wind it travels at a speed of 150-x miles per hour with respect to the ground.
In a period of time of t hours, the plane will flew
t%28150%2Bx%29=300 miles with the wind, and
t%28150-x%29=200 miles against the wind.
So,
t%28150%2Bx%29%2F%28t%28150-x%29%29=300%2F200--->%28150%2Bx%29%2F%28150-x%29=3%2F2--->2%28150%2Bx%29=3%28150-x%29--->300%2B2x=450-3x%29--->2x%2B3x=450-300%29--->5x=150%29--->x=150%2F5%29--->highlight%28x=30%29
The speed of the wind was 30 miles per hour.