Question

Translate to a system of equations and then solve: A commercial jet can fly 1728 miles in 4 hours with a tailwind but only 1536 miles in 4 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 408 mph and the speed of the wind is 24 mph.

Step-by-step solution

Given Information 

A commercial jet can fly 1728 miles in 4 hours with a tailwind but only 1536 miles in 4 hours into a headwind.

Assume variables 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.

A commercial jet can fly 1728 miles in 4 hours with a tailwind but only 1536 miles in 4 hours into a headwind.

Distance = 1728 and time is 4 hours

Distance = speed * time

$$\begin{gathered} 4(j+w)=1728 \\ j+w=432 \end{gathered}$$

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

Distance =1536 and time is 4 hours

$$\begin{gathered} 4(j-w)=1536 \\ j-w=384 \end{gathered}$$

solve the equations

$$\begin{gathered} j+w=432 \\ j-w=384 \\ ------ \\ 2j=816 \\ j=408 \\ j+w=432 \\ 408+w=432 \\ w=432-408 \\ w=24 \end{gathered}$$

The speed of the jet is 408 mph and the speed of the wind is 24 mph.