A plane flies 390 miles with the wind and 325 miles against the wind in the same length of time. If the speed of the wind is 10 mph, find the speed of the plane in still air.

Question

The speed of the plane is still air is blank mph

I got 110 mph

Is that correct?

Answer 1

When the plane flies with the wind its speed is p+10 where p is the plane's speed in still air. When it flies against the wind its speed is p-10. s=vt, where s=distance (miles), v is speed (mph), t is time (hours).

t=s/v, so, since the times are the same for the two distances, 390/(p+10)=325/(p-10).

Cross-multiplying: 390(p-10)=325(p+10), 390p-3900=325p+3250, 65p=7150, p=7150/65=110mph.

So the plane's speed in still air is 110mph, as you thought. (Time is 3¼ hours.)