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

Question 1057141: A plane has a cruising speed of 150 mph when there is no wind. At this speed, the 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.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Your description is not written the way you mean.

"At this speed", the two directions either had no wind; or the direction of the wind switched between the two trip parts. Drop the phrase and your description is good enough.

SPEED TIME DISTANCE WITHWIND r+w t p AGAINSTW r-w t d

Unknown variables are w and t. The question asks for w.

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
A plane has a cruising speed of 150 mph when there is no wind. At this speed, the 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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let "v" be the speed of the wind, in mph. Then the speed of the plane flying with the wind is (150+v) mph. The time it spends to cover 300 miles is hours. The speed of the plane flying against the wind is (150-v) mph. The time it spends to cover 200 miles is hours. The condition says = . To solve it, multiply both sides by (150+v)*(150-v). You will get 300*(150-v) = 200*(150+v). Cancel the factor 100 in both sides. You will get 3*(150-v) = 2*(150+v). Simplify: 450 - 3v = 300 + 2v, or 450 - 300 = 2v + 3v, or 5v = 150. Then v = = 30 mph. Answer. The wind speed is 30 mph.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A plane has a cruising speed of 150 mph when there is no wind. At this speed, the 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.

Same concept used in problem # 1057070.
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