# An airplane flies 1,050 km with the wind.  In the same amount of time, it can fly 750 km against the wind.  The speed of the plane in still air is 200 km/h.  Find the speed of the wind.

jeew-m | College Teacher | (Level 1) Educator Emeritus

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Airplane = A

Wind = W

Velocity = V

Case (1)

When the air plane goes with wind

Assume wind and airplane goes` rarr` direction.

`rarrV_1 = rarrV_A+rarrV_W`

` V_1 = V_A+V_W`

Since it travels 1050km in time t

`V_1xxt = 1050`

`(V_A+V_W)xxt = 1050 ---(1)`

Case (2)

When the air plane goes against wind

Air plane goes `larr ` and wind goes `rarr`

`larrV_2 = larrV_A+rarrV_W`

`larrV_2 = larrV_A-larrV_W`

`rarr-V_2 = -V_A+V_W`

`rarrV_2xxt = -750`

`(V_W-V_A)xxt = -750 ----(2)`

`((1))/((2))`

`(V_A+V_W)/(V_W-V_A) = 1050/(-750)`

It is given that `V_A = 200`

`(200+V_W)/(V_W-200) = 1050/-750`

`-5(200+V_W) = 7(V_W-200)`

`12V_W = 400`

`V_W = 33.33`

We considered for the first case that airplane runs to `rarr` direction.

So the wind is at the `rarr` direction with a speed of 33.33km/h