Question

A jet travels 6096 miles against a jetstream in 8 hours and 6736 miles with the jetstream in the same amount of time. What is the rate of the jet in still air andwhat is the rate of the jetstream?

Answer 1

The rate of the jet in still air is 802 mph and the speed of the jetstream is 40 mph

Explanation:

Given:

Let

x = the jet rate at no wind (in mph)

y = the rate of the wind.

Therefore:

`\begin{gathered} (6096)/(8)=x-y\rightarrow x=762+y\text{ (1)} \\ (6736)/(8)=x+y\rightarrow x=842-y\text{ (2)} \end{gathered}`

We solve the system by means of the matching method, equating both equations like this:

`\begin{gathered} 762+y=842-y \\ 2y=842-762 \\ y=(80)/(2) \\ y=40\text{ mph} \\ \\ in\text{ this case of :} \\ x=762+40 \\ x=802\text{ mph} \end{gathered}`

The rate of the jet in still air is 802 mph and the speed of the jetstream is 40 mph.