Question

A private jet can fly 1,210 miles against a 25-mph headwind in the same amount of time it can fly 1694 miles with a 25-mph tailwind. Find the speed of the jet.

Answer 1

Answer:

The speed of the jet is 150 mph

Step-by-step explanation:

Let x represent the speed the jet.

The speed of the wind is 25 mph

Let t represent the time

Given that the jet can fly 1210 miles against the headwind, then

`\begin{gathered} x-25=(1210)/(t) \\ \\ x=25+(1210)/(t)\ldots\ldots...\ldots\ldots\ldots......\ldots\ldots....(1) \end{gathered}`

It can fly 1694 miles against the tailwind, then

`\begin{gathered} x+25=(1694)/(t) \\ \\ x=(1694)/(t)-25\ldots\ldots......\ldots\ldots\ldots......\ldots\ldots\ldots(2) \end{gathered}`

From (1) and (2)

`\begin{gathered} 25+(1210)/(t)=(1694)/(t)-25 \\ \\ \text{Multiply both sides by t} \\ 25t+1210=1694-25t \\ 25t+25t=1694-1210 \\ 50t=484 \\ t=(484)/(50)=9.68 \end{gathered}`

With t = 9.68 hours, we can find x by sustituting the value into either of (1) or (2)

Using (2)

`\begin{gathered} x=(1694)/(9.68)-25 \\ \\ =150 \end{gathered}`

The speed of the jet is 150 mph