Aplane has a cruising speed of 250 miles per hour when there is no wind. at this speed, the plane flew 300 miles with the wind in the same amount of time it flew 200 miles against the wind. find the speed of the wind.

V = speed of the plane with no wind = 250 mph

v = speed of wind  

consider the motion of the plane while traveling with the wind :

V' = speed of plane travelling in the direction of wind = V + v = 250 + v

d' = distance traveled = 300 miles  

t' = time taken to travel the distance  

time taken to travel the distance is given as  

t' = d'/V'

t' = 300/(250 + v)                                           eq-1

consider the motion of the plane while traveling against the wind :

V'' = speed of plane travelling against the direction of wind = V - v = 250 - v

d'' = distance traveled = 200 miles  

t'' = time taken to travel the distance  

time taken to travel the distance is given as  

t'' = d''/V''

t'' = 200/(250 - v)                                           eq-2

Given that :

time taken to travel 300 miles = time taken to travel 200 miles  

t' = t''

using eq-1  and eq-2

300/(250 + v)  = 200/(250 - v)

3/(250 + v)  = 2/(250 - v)

750 - 3 v = 500 + 2 v  

5 v = 250

v = 50 mph