Question

A plane traveled 1248 miles to Ft. Worth and back. The trip there was with the wind. It took 12

hours. The trip back was into the wind. The trip back took 24 hours. What is the speed of the
plane in still air? What is the speed of the wind?

Answer 1

speed of the plane in still air is 76 m/s and speed of the wind is 28 m/s .

Explanation:

Here we have , A plane traveled 1248 miles to Ft. Worth and back. The trip there was with the wind. It took 12 hours. The trip back was into the wind. The trip back took 24 hours. We need to find What is the speed of the plane in still air? What is the speed of the wind? Let's find out :

For Going trip :

Let speed of plane be u , and wind be v so : Speed = ( Distance ) / ( time )

⇒
`u+v = (1248)/(12)`

⇒
`u+v = 104` ...........(1)

For Returning Trip :

⇒
`u-v = (1248)/(24)`

⇒
`u-v = 52` ...........(2)

Adding both equations we get :

⇒
`(u+v)+(u-v)=104+52`

⇒
`2u=156`

⇒
`u= 76m/s`

Putting this value in equation (1) we get :

⇒
`76+v = 104`

⇒
`v=28m/s`

Therefore , speed of the plane in still air is 76 m/s and speed of the wind is 28 m/s .