Question

An Airbus A320 jet flies 5 hours west with a 40-mph tailwind. Returning against the wind takes 7 hours. Find the speed of the jet with no wind.

Answer 1

The speed of the jet with no wind is 240 miles per hour.

Explanation:

The speed of the jet with no wind is equivalent to the speed of the jet relative to wind. Physically speaking, we have the following system of linear equations under the assumption that both speeds of wind and jet are constant:

In favor of wind

`(s)/(t_(F)) = v_(W)+v_(J/W)` (1)

Against wind

`-(s)/(t_(A)) = v_(W) -v_(J/W)` (2)

Where:

`s` - Travelled distance, measured in miles.

`t_(F)`,
`t_(A)` - Time, measured in hours.

`v_(W)` - Wind speed, measured in miles per hour.

`v_(J/W)` - Jet speed relative to wind, measured in miles per hour.

If we know that
`t_(F) = 5\,h`,
`t_(A) = 7\,h`,
`v_(W) = 40\,(mi)/(h)`, then the speed of the jet with no wind is:

`(s)/(5) = 40 + v_(J/W)` (3)

`-(s)/(7) = 40-v_(J/W)` (4)

`(s)/(5)-40 = 40 +(s)/(7)`

`(s)/(5)-(s)/(7) = 80`

`(7\cdot s - 5\cdot s)/(35) = 80`

`2\cdot s = 2800`

`s = 1400\,mi`

From (3), we find that speed of the jet with no wind is:

`v_(J/W) = (s)/(5)-40`

`v_(J/W) = (1400)/(5)-40`

`v_(J/W) = 240\,(mi)/(h)`

The speed of the jet with no wind is 240 miles per hour.