Question

A pilot can travel for 140 miles with the wind in the same amount of time as 360 miles against the wind. Find the speed of the wind if the pilot speed in still air is 200 mph.

Answer 1

Answer:

  -88 mph

Step-by-step explanation:

We can use the relation ...

  time = distance/speed

to compare the times in the two directions.

  $\dfrac{140}{200+w}=\dfrac{360}{200-w}\\\\140(200-w)=360(200+w)\\\\200(140-360)=w(360+140)\\\\w=\dfrac{200(-220)}{500}=-88 \quad\text{miles per hour}$

The wind speed is -88 miles per hour.

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The problem statement tells us the travel is slower with the wind than against the wind. Hence "with the wind" must be subtracting from the net speed. That is, the wind speed is negative.