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?
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 (v-w)*6.25 = 3400
in case 2, speed = (v+w) mph. time = 5 h. d = 3400 m, therefore (v+w)*5 = 3400
2 linear equations in two variables, can be solved to get: v = 612 mph and w = 68 mph.
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