Question

A jet travels 1983 miles against a jetstream in 3 hours and 2373 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?Solve using a system of linear equations

Answer 1

Let:

x = Speed of the jet

y = Speed of jetstream

so:

$1983=3x-3y_{\text{ }}(1)$

and

$2373=3x+3y_{\text{ }}(2)$

Solve the system using elimination method:

$\begin{gathered} (1)+(2) \\ 1983+2373=3x+3x-3y+3y \\ 4356=6x \\ x=\frac{4356}{6} \\ x=726mph \end{gathered}$

Replace x into (1)

$\begin{gathered} 1983=3(726)-3y \\ 1983=2178-3y \\ 195=3y \\ y=\frac{195}{3} \\ y=65mph \end{gathered}$

Answer:

Rate of the jet in still air: 726 mph

Rate of the jetstream: 65mph