Question

at maximum speed, an airplane travels 1680 miles against the wind in 5 hours. Flying with the wind, the plane can travel the same distance in 4 hours.

Answer 1

d=vt

1680=5(p-w)

p-w=336

1680=4(p+w)

p+w=420

p-w+p+w=336+420

2p=756

p=378 mph, and since w=420-p

w=42 mph

So the plane's velocity in still air is 378 mph and the wind speed is 42mph.

Answer 2

Answer: The speed of wind is 378 mph.

The speed of airplane is 42 mph.

Explanation:

Distance an airplane travels = 1680 miles

Against the wind in 5 miles,

Let the speed of wind be x

Let the speed of airplane be y.

So, for against the wind , it becomes,

`(1680)/(5)=x-y\\\\336=x-y--------(1)`

similarly,

with the wind , it becomes,

`(1680)/(4)=x+y\\\\420=x+y------(2)`

From Eq(1) and Eq(2), we get,

`x-y=336\\x+y=420\\-----------------\\2x=756\\\\\implies x=(756)/(2)=378\ mph`

Hence, the speed of wind is 378 mph.

The speed of airplane is given by

`y=420-378=42\ mph`