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

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

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

It can fly 1694 miles against the tailwind, then

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

From (1) and (2)

$\begin{gathered} 25+\frac{1210}{t}=\frac{1694}{t}-25 \\ \\ \text{Multiply both sides by t} \\ 25t+1210=1694-25t \\ 25t+25t=1694-1210 \\ 50t=484 \\ t=\frac{484}{50}=9.68 \end{gathered}$

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

Using (2)

$\begin{gathered} x=\frac{1694}{9.68}-25 \\ \\ =150 \end{gathered}$

The speed of the jet is 150 mph