Question

Matt and Anna are frequent flyers they often fly between two cities that are a distance of 800 miles apart. On one particular trip they flew into the wind and the trip took 2.5 hours. The return trip with the wind behind them only took about 2 hours . Find the speed of the wind and the speed of the plane in still air.

Answer 1

Let the speed of plane in still air be x miles per hour
Let the speed of air be y miles per hour

While going,
time taken = distance / relative speed
2.5 = 800 / (x-y)
x-y = 320 ..eqn 1

While returning,
time taken = distance / relative speed
2 = 800 / (x+y)
x+y = 400 ..eqn 2

add eqn 1 and eqn 2:
x-y+x+y = 320+400
2x = 720
x = 360 mph

put this in eqn 1
x-y = 320
360-y = 320
y = 40 mph

Answer:
speed of the wind = 40 mph
speed of the plane in still air = 360 mph