Respuesta :
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
