In the following exercises, translate to a system of equations and solve.

A small jet can fly 1,435 miles in 5 hours with a tailwind but only 1215 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

The given data is that a small jet can fly 1,435 miles in 5 hours with a tailwind but only 1215 miles in 5 hours into a headwind.

Let x be the rate of the jet with tailwind and y be the rate of headwind.

The jet fly with tailwind for 5 hours and the distance covered is 1435 miles and the actual rate of jet is $x+y$and the distance covered can be expressed as $5(x+y)=1435--\left(1\right)$

The jet fly with headwind for 5 hours and distance covered is 1215 miles. So, the actual rate of the jet is $x-y$and the distance covered is$5(x-y)=1215--\left(2\right)$

Solve the equations (1) and (2) by adding both the equations.

$$\begin{gathered} 5x+5y+5x-5y=1435+1215 \\ 10x=2650 \\ x=265 \end{gathered}$$

Substitute the value of x in equation (1) to get the value of y.

$$\begin{gathered} 5\left(265\right)+5y=1435 \\ 5y=1435-1325 \\ 5y=110 \\ y=22 \end{gathered}$$