Question

Translate to a system of equations and then solve: A small jet can fly 1,325 miles in 5 hours with a tailwind but only 1035 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Short answer

The speed of the jet is 236 mph and the speed of the wind is 29 mph.

Step-by-step solution

Given Information 

A small jet can fly 1,325 miles in 5 hours with a tailwind but only 1035 miles in 5 hours into a headwind.

Assume variable and frame equations

Let j = the speed of the jet in still air.

w = the speed of the wind

In a tailwind, the wind helps the jet and so the rate is j + w.

Distance = 1325 and time is 5 hours

Distance = speed * time

$5(j+w)=1325$

In a headwind, the wind slows the jet and so the rate is j − w.

Distance = 1035 and time is 5 hours

$5(j-w)=1035$

solve both the equations

$$\begin{gathered} 5(j+w)=1325 \\ j+w=265 \\ 5(j-w)=1035 \\ j-w=207 \\ j+w=265 \\ ------ \\ 2j=472 \\ divideby2 \\ j=236 \\ j+w=265 \\ 236+w=265 \\ w=265-236 \\ w=29 \end{gathered}$$

The speed of the jet is 236 mph and the speed of the wind is 29 mph.