A plane can fly 290 miles downwind in the same amount of tim

A plane can fly 290 miles downwind in the same amount of time as it can travel 220 miles upwind. Find the velocity of the wind if the plane can fly 255 mph in still air.

Solution

t = distance/speed

let the speed of wind v mph

speed downwind = (225+v) mph
t = distance/speed
= 290/(225+v) ....eqn 1

speed upwind = (225-v) mph
t = distance/speed
= 220/(225-v) ...eqn 2

equate eqn 1 and eqn 2 as both are equal time
290/(225+v) = 220/(225-v)
290*(225-v) = 220*(225+v)
65250 - 290*v = 49500 + 220*v
510*v = 15750
v = 30.9 mph

Answer: 30.9 mph