A jet travels 4340 mi against a jetstream in 7 hours and 5180 mi 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?

Answer 1

The first step to solving this problem is to find the difference in distance traveled between the two planes so...

5180mi-4340mi=840mi

Now keep in mind that this distance has accumulated over the 7 hours of travel so to find difference in distance travelled by the two planes per hour we can take the 840mi and divide it by 7 to get the difference in distance travelled by the two planes after 1 hour. So...

840mi/7hr= 120mi/hr.

This however is not the rate of the jet stream. This is the difference in distance traveled by the two planes after 1 hour now keep in mind that both planes are affected by the jet stream equally however one is going with the stream and one is going against it. What this means is that one plane is traveling faster and the other is traveling slower by the rate of the jet stream. So if you divide the distance of 120mi by two you could then say that one plane is traveling 60 miles/hr slower and the other is traveling 60miles/hr faster you can also note that the difference between -60 and 60 is 120. Now that you know the rate of the jet stream(60mi/hr) you can multiply this amount by the course of 7 hours and subtract it from 5180 or you can add it to 4340 either way you will get the same answer and rightly so because the rate of the plane remains the same in still air, the jet-stream is what causes the plane to go faster or slower.

5180-(60*7)=4760

or

4340+(60*7)=4760

thus the rate of the plane is 4760mi/7hrs

or 680mi/hr

Answer 2

4340 = (S-r)*7 = 7s - 7r

5180 = (S+r)*7 = 7s + 7r

9520 = 14s

s=680

4340 = 7*680 - 7r

4340 - 7*680 = -7r

-420 = -7r

r = 60