Question

A plane traveled 1794 miles to Bangkok and back. The trip there was with the wind. It took 13 hours. The trip back was into the wind. The trip back took 23 hours. Find the speed of the plane in still air and the speed of the wind.​

Answer 1

The speed of wind is 30 miles/hour

Speed of plane in still air is 108 miles /hour

Explanation:

Distance traveled by plane to Bangkok = 1794 miles

The trip there was with the wind. Time taken = 13 hours.

The trip back was into the wind. The trip back took 26 hours.

Let s = plane speed in still air

let w = speed of the wind

(s+w) = speed of plane with wind

(s-w) = speed of plane against wind

Distance = Speed * Time

When the trip was with the wind .

⇒
`1794 =(s+w)*13`

⇒
`(1794)/(13)=s+w`

⇒
`138=s+w` ---1

When The trip back was into the wind.

⇒
`1794 =(s-w)*23`

⇒
`(1794)/(23)=s-w`

⇒
`78=s-w` ---2

Add 1 and 2

⇒s+w+s-w =138+78

⇒2s =216

⇒
`s=(216)/(2)`

⇒
`s=108`

To find w substitute the value of s in 1

⇒
`138=108+w`

⇒
`138-108=w`

⇒
`30=w`

Thus the speed of wind is 30 miles/hour

Speed of plane in still air is 108 miles /hour