Question

A commercial jet can fly 1342 miles in 5.5 hours with a tailwind but only 1078 miles in 5.5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Answer 1

.Explanation

Let the speed of the still wind be V

let the speed of the wind be W

From the first statement

`\begin{gathered} v+w=(1342)/(5.5) \\ \end{gathered}`

From the second statement

`v-w=(1078)/(5.5)`

The value of v and w will be obtained by solving using the elimination method

`\begin{gathered} \text{Adding both equations} \\ v+v+w-w=(1342)/(5.5)+(1078)/(5.5) \end{gathered}`

Thus

`\begin{gathered} 2v=(1342+1078)/(5.5) \\ \\ 2v=(2420)/(5.5) \\ \\ v=(2420)/(11) \\ \\ v=220 \end{gathered}`

Then to get W

`\begin{gathered} v+w=(1342)/(5.5) \\ \\ w=(1342)/(5.5)-v \\ \\ w=(1342)/(5.5)-220 \\ \\ w=24 \end{gathered}`

Therefore, the speed of the jet in the still air is 220 miles per hour

The speed of the wind is 24 miles per hour