Question

A commercial jet can fly 868 miles in 2 hours with a tailwind but only 792 miles in 2 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Answer 1

The speed of the jet in still air is 415 mph and the speed of the wind is 19 mph

Answer 2

The speed of the jet in still air is 415 mph and the speed of the wind is 19 mph

Explanation:

we know that

The speed is equal to divide the distance by the time

Let

x -----> the speed of the wind in miles per hour

y ----> the speed of the jet in still air in miles per hour

we know that

With a tailwind

`y+x=(868)/(2)`

`y+x=434` ----> equation A

With a headwind

`y-x=(792)/(2)`

`y-x=396` ----> equation B

solve the system of equations A and B by elimination

Adds equation A and equation B

`y+x=434\\y-x=396\\------\\y+y=434+396\\2y=830\\y=415`

Find the value of x

`y+x=434`

`415+x=434`

`x=434-415`

`x=19`

therefore

The speed of the jet in still air is 415 mph and the speed of the wind is 19 mph