A plane flying with the wind flew 360 miles in 3 hours.

[tseday871221]

A plane flying with the wind flew 360 miles in 3 hours. Against the wind, the plane required 4 hours to fly the same distance. Find the rate of the plane in calm air and the rate of the wind.

 

[arthur ohlsten]

let P be planes speed in still air
let w be wind speed
360/[P+w]=3
360/[P-w]=4

360=3P+3w
360=4P-4w

multiply first equation by 4 and second by 3
1440=12P+12w
1080=12P-12w

add the equations
2520=24P
P=105 mph answer

subtract eq2 from eq1
360=24w
w=15mph answer

Arthur