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.

Step-by-step 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

$\frac{x+y}{2}$

Speed of  the wind be

$\frac{x-y}{2}$

According to question,

Speed of downstream is given by

$x=\frac{720}{3}=240\ mph$

Speed of upstream is given by

$y=\frac{720}{4}=180\ mph$

So, Speed of plane in still air is given by

$\frac{x+y}{2}=\frac{240+180}{2}=210\ mph$

Speed of wind is given by

$\frac{x-y}{2}=\frac{240-180}{2}=30\ mph$

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