Question

Flying against the wind, a jet travels 2160 miles in 3 hours. Flying with the wind, same jet travels 6000 miles in 6 hours. What is the rate of the jet in still air and what rate of the wind?

Answer 1

The velocity of jet in still air is
`860miles/hour` and velocity of wind is
`140miles/hour`.

Explanation:

Let x be the rate of the jet in still air and y be the rate of the wind.

Given:

Velocity against wind, a jet travels 2160 miles in 3 hours.

Velocity against wind
`=(2160)/(3) = 720 miles/hour`

Flying with the wind, same jet travels 6000 miles in 6 hours.

Flying with the wind
`=(6000)/(6) = 1000 miles/hour`

As such its velocity against wind is
`x-y`

and with wind is
`x+y` therefore

`x-y=720`------------(1)

`x+y=1000`---------------(2)

Adding equation 1 and 2.

`2x=1720`

`x=(1720)/(2)`

`x=860`

Put x value in equation 2

`860+y=1000`

`y=1000-860`

`y=140`

Hence velocity of jet in still air is
`860miles/hour` and velocity of wind is
`140miles/hour`.