Question

A jet travels 5008 miles against a jetstream in 8 hours and 5968 miles with the jetstream in the same amount of time. What is the rate of the jet in still air andwhat the rate of the jetstream?

Answer 1

Let's use the variable x to represent the jet speed and y to represent the jetstream speed.

If the jet travels 5008 miles in 8 hours against the jetstream (that is, a relative speed of x - y), we can write the equation:

`\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ 5008=(x-y)\cdot8 \\ x-y=626 \end{gathered}`

Then, if the jet travels 5968 miles in 8 hours with the jetstream (relative speed of x + y), so we have:

`\begin{gathered} 5968=(x+y)\cdot8 \\ x+y=746 \end{gathered}`

Adding the equations we found, we can find the value of x:

`\begin{gathered} x-y+(x+y)=626+746 \\ x-y+x+y=1372 \\ 2x=1372 \\ x=(1372)/(2) \\ x=686 \\ \\ x-y=626 \\ 686-y=626 \\ y=686-626=60 \end{gathered}`

So the jet speed is 686 mph and the jetstream speed is 60 mph.