A pilot can travel 385 miles with the wind in the same amoun

A pilot can travel 385 miles with the wind in the same amount of time as 315 miles against the wind. Find the speed of the wind if the pilot\'s speed in still air is 180 per hour.

Solution

Let the speed of the wind be w

and travel time be t

Then we can say
(180+w) = effective speed with the wind
and
(180-w) = effective speed against the wind

dist = time * speed

385 = t * (180+w) ====> 385 = 180 t + tw ======> (1)

315 = t * (180-w) ====> 315 = 180 t - tw

adding the above equations

360 t = 700 =====> t = 1.94444

substituting in (1)

w = (385/1.94444) - 180

= 198 - 180

= 18