Question

A small plane can fly 720 miles with the wind in 3 hours and can make the return trip in 4 hours. Find the speed of the plane in still air and the speed of the wind.

Answer 1

Answer: Speed of the plane in still air is 210 mph and Speed of the wind is 30 mph.

Explanation:

Since we have given that

A small plane can fly 720 miles with the wind in 3 hours and can make the return trip in 4 hours.

Let the speed downstream be x

Let the speed of upstream be y

So, Speed of of the plane in still air be

`(x+y)/(2)`

Speed of the wind be

`(x-y)/(2)`

According to question,

Speed of downstream is given by

`x=(720)/(3)=240\ mph`

Speed of upstream is given by

`y=(720)/(4)=180\ mph`

So, Speed of plane in still air is given by

`(x+y)/(2)=(240+180)/(2)=210\ mph`

Speed of wind is given by

`(x-y)/(2)=(240-180)/(2)=30\ mph`

Hence, Speed of the plane in still air is 210 mph and Speed of the wind is 30 mph.