Q 120 - Intermediate Algebra

Question

A small jet can fly $1072$ miles in $4$ hours with a tailwind but only $848$ miles in $4$ hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Step-by-Step Solution

Answer

The speed of the jet in still air is $240$ mph.

The speed of the wind is $28$ mph.

Step 1. Given information.

Consider the given question,

A jet can fly a distance of $1072$ miles in $4$ hours with a tailwind.

It can fly $848$ miles in $4$ hours with a headwind.

Assume $x$ to be the speed of the jet in still air and $y$ to be the speed of the wind.

Step 2. Form the equations.

Consider the given question,

When the jet flies $1072$ miles in $4$ hours with a tailwind in which the wind helps the jet.

So,$$\begin{gathered} 4\left(x+y\right)=1072 \\ x+y=268 ...... \left(i\right) \end{gathered}$$

When the jet flies $848$ miles in $4$ hours with a headwind in which the wind slows the jet.

So, $$\begin{gathered} 4\left(x-y\right)=848 \\ x-y=212 ...... \left(ii\right) \end{gathered}$$

Step 3. Solve the equations.

Add equations (i) and (ii),

$$\begin{gathered} \left(x+y\right)+\left(x-y\right)=268+212 \\ 2x=480 \\ x=240 \end{gathered}$$

Substituting $x=240$ in equation (ii),

$$\begin{gathered} 240-y=212 \\ y=28 \end{gathered}$$

Step 4. Check the answers.

Substitute the values in equation (i),

$$\begin{gathered} 240+28=268 \\ 268=268 \end{gathered}$$

This is true.

Substitute the values in equation (ii),

$$\begin{gathered} 240-28=212 \\ 212=212 \end{gathered}$$

This is true.

The speed of the jet in still air is $240$ mph.

The speed of the wind is $28$ mph.