a plane travels 4125 miles with the wind in 7.5 hours and 3525 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

Question

a plane travels 5100 miles with the wind in 7.5 hours and 4200 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

Answer 1

With the wind the plane travels 4125 miles in 7.5 hrs for an average speed 550 mph.

Against the wind the same plane travels 3525 miles in 7.5 hrs for an average speed of 470 mph.

Since we are assuming the wind is constant we can take the average of the two and find the planes speed in still air to be 510 mph and the wind speed would be 40 mph. ( 550 mph - 510 mph)

Answer 2

4125 miles with the wind in 7; 1/2 hours

3525 against the wind in the same time

distance = time times speed

d = rt

4125 = 7.5(p+w)

3525 = 7.5(p-w)

add them

7650 = 15p

p = 7650/15 = plane speed in still air = 510 mph

-w = 3525/7.5 - 510 = 470-510=-40

w= wind speed = 40 mph

5100 = 7.5(p+w_

4200= 7.5(p-w)

9300=15p

p=9300/15= plane speed in still air= 620 mph

-w=4200/7.5 -620=-60

w= 60mph= wind speed