SOLUTION: A plane can fly 160 mph in calm air. Flying with the wind, the plane can fly 500 miles in the same amount of time required to fly 420 miles against the wind. What is the speed of t

Question 260910: A plane can fly 160 mph in calm air. Flying with the wind, the plane can fly 500 miles in the same amount of time required to fly 420 miles against the wind. What is the speed of the plane? ok so the answer is supposed to be 13.9 mph but i don't know how to set up me equations.
Answer by Greenfinch(383) (Show Source): You can put this solution on YOUR website!
Speed against wind is 160 - v
Speed with wind is 160 + v
Time to fly 500 miles with wind is 500/(160 1+ v)
Time to fly 420 mile against wind is 420/(160 - v)
And they are equal
so 500/(160 + v) = 420/(160 - v)
multiplying up
500x(160 - v) = 420x(160 + v)
80,000 - 500v = 67200 + 420v
12800 = 920v
v = 12800/920 = 13.913 mph
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