# An airplane flying into a headwind travels 3400 miles in 6 hours and 15 minutes. on the return flight, the same distance is traveled in 5 hours. Find the speed of the plane in still air(in mph). Also find the speed of the wind(mph).Assuming that both remain constant throughout the round trip?

An airplane flying into a headwind travels 3400 miles in 6 hours and 15 minutes. on the return flight, the same distance is traveled in 5 hours. Find the speed of the plane in still air(in mph). Also find the speed of the wind(mph).Assuming that both remain constant throughout the round trip?
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Krha77
Let the speed of plane in still air be v mph. Speed of wind in w mph. When airplane flies into headwind, the velocity vectors of wind and plane are in opposite direction, hence the net velocity is (v-w) mph. On the return, both velocity vectors are in the same direction, hence (v+w) mph.
in case 1, speed = (v-w) mph. time = 6.25 h. d = 3400 m, therefore $\left(v-w\right)\cdot 6.25=3400$
in case 2, speed = (v+w) mph. time = 5 h. d = 3400 m, therefore $\left(v+w\right)\cdot 5=3400$
2 linear equations in two variables, can be solved to get: v = 612 mph and w = 68 mph.