what is the rate of the jets in still air and what is the rate of the jetstream?

Question

a jet travels 5904 miles against a jetstream in 8 hours and 7264 miles with the jetstream in the same amount of time. what is the rate of the jets in still air and what is the rate of the jetstream?

Answer 1

First thing we want to do is call some variables. Let's let

 

Rj = rate of jet

Rs = rate of stream

 

We know that distance = rate*time. In your first scenario, the jet-stream is working against you, so it'll subtract from your rate. In the second scenario, the jet-stream is working in your favor, so it'll add to your rate.

 

Scenario 1:

 

8 hours * (Rj mph - Rs mph) = 5904 miles

 

Scenario 2:

 

8 hours * (Rj mph + Rs mph) = 7264 miles

 

Rj - Rs = 738

Rj + Rs = 908

 

Two equations, two unknowns; just what we want!

 

Let's add the two equations together:

 

Rj - Rs + Rj + Rs = 738 + 908

 

2Rj = 1646

Rj = 823 mph

 

Rs = Rj - 738

Rs = 823 - 738

 

Rs = 85mph

 

So your jet in still air travels 823 mph, and the jet-stream is moving at 85 mph.

 

Always good to check your work:

 

Consider Scenario 1, where the jet-stream is working against you.

 

823 mph - 85 mph = 738mph

 

In the course of 8 hours at this speed, you should travel 5904 miles.

 

738 * 8 = 5904 miles. Check.

 

Now consider Scenario 2, where the jet-stream is working with you.

 

823 mph + 85 mph = 908 mph

 

In the course of 8 hours at this speed, you should travel 7264 miles.

 

908 * 8 = 7264 miles. Checkmate.

 

Hope this helps.