s2vunov

2022-09-06

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?

Krha77

Beginner2022-09-07Added 8 answers

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 $$(v-w)\cdot 6.25=3400$$

in case 2, speed = (v+w) mph. time = 5 h. d = 3400 m, therefore $$(v+w)\cdot 5=3400$$

2 linear equations in two variables, can be solved to get: v = 612 mph and w = 68 mph.

in case 1, speed = (v-w) mph. time = 6.25 h. d = 3400 m, therefore $$(v-w)\cdot 6.25=3400$$

in case 2, speed = (v+w) mph. time = 5 h. d = 3400 m, therefore $$(v+w)\cdot 5=3400$$

2 linear equations in two variables, can be solved to get: v = 612 mph and w = 68 mph.

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