Question

Flying against the wind, a jet travels 8320 miles in 8 hours. Flying with the wind, the same jet travels 11,700 miles in 9 hours. What is the rate of the jet in stillair and what is the rate of the wind?

Answer 1

Consider the relation,

`\text{Time}=\frac{\text{ Distance}}{\text{ Speed}}`

Let 'x' be the speed of jet in still air, and 'y' be the rate of the wind flow.

When flying against the wind, the net speed of the jet will be (x-y) mph.

Given that the jet takes 8 hours to travel 8320 miles against the wind,

`\begin{gathered} 8=(8320)/(x-y) \\ x-y=(8320)/(8) \\ x-y=1040\ldots\ldots\ldots(1) \end{gathered}`

When flying with the wind, the net speed of the jet becomes (x+y) mph.

Given that the jet takes 9 hours to travel 11700 miles along the wind,

`\begin{gathered} 9=(11700)/(x+y) \\ x+y=(11700)/(9) \\ x+y=1300\ldots\ldots\ldots(2) \end{gathered}`

Add the equations (1) and (2) as follows,

`\begin{gathered} (x-y)+(x+y)=1040+1300 \\ 2x=2340 \\ x=1170 \end{gathered}`

Substitute this value in equation (1) to obtain the other variable,

`\begin{gathered} 1170-y=1040 \\ y=1170-1040 \\ y=130 \end{gathered}`

So the solution to the pair of equations is,

`(x,y)=(1170,130)`

Thus, the rate of jet in still air is 1170 mph, and the rate of the wind is 130 mph.