Flying against the wind, a jet travels 3040 miles in 4 hours. Flying with the wind, the same jet travels 8260 miles in 7 hours. What is the rate of the jet in still air, and what is the rate of the wind?

Jun 16, 2018

Velocity of jet in still air is $970$ miles per hour and velocity of wind is $210$ miles per hour.

Explanation:

Jet's velocity against wind is $\frac{3040}{4} = 760$ mile per hour and flying with wind it is $\frac{8260}{7} = 1180$ miles per hour.

Let the velocity of jet in still air be $x$ miles per hour and velocity of wind be $y$ miles per hour.

As such its velocity against wind is $x - y$ and with wind is $x + y$ and therefore

$x - y = 760$ and $x + y = 1180$

Adding the two $2 x = 1940$ and $x = 970$

and $y = 1180 - 970 = 210$

Hence velocity of jet in still air is $970$ miles per hour and velocity of wind is $210$ miles per hour.