Question

A jet travels 2301 miles against the wind in 3 hours and 2811 miles with the wind in the same amount of time. What is the rate of the jet in still air and what is the rate of the wind

Answer 1

Answer:

The rate of the jet in still air is 852 miles per hour. The rate of the wind is 85 miles per hour.

Step-by-step explanation:

Let suppose that jet travels uniformly, that is, at constant speed, the expressions for its travels against the wind and with the wind are, respectively:

Against the wind

$v -u = \frac{\Delta x_{1}}{\Delta t_{1}}$

With the wind

$v +u = \frac{\Delta x_{2}}{\Delta t_{2}}$

Where:

$v$ - Speed of the jet in still air, measured in miles per hour.

$u$ - Speed of wind, measured in miles per hour.

$\Delta x_{1}$, $\Delta x_{2}$ - Distances travelled by jet against the wind and with the wind, measured in miles.

$\Delta t_{1}$, $\Delta t_{2}$ - Times against the wind and with the wind, measured in hours.

By adding both expressions:

$2\cdot v = \frac{\Delta x_{1}}{\Delta t_{1}}+\frac{\Delta x_{2}}{\Delta t_{2}}$

$v = \frac{1}{2}\cdot \left(\frac{\Delta x_{1}}{\Delta t_{1}} + \frac{\Delta x_{2}}{\Delta t_{2}} \right)$

Given that $\Delta x_{1} = 2301\,mi$, $\Delta t_{1} = 3\,h$, $\Delta x_{2} = 2811\,mi$ and $\Delta t_{2} = 3\,h$, the speed of the jet is:

$v = \frac{1}{2}\cdot \left(\frac{2301\,mi}{3\,h}+\frac{2811\,mi}{3\,h} \right)$

$v = 852\,\frac{mi}{h}$

The rate of the jet in still air is 852 miles per hour.

Lastly, the rate of the wind is:

$u = \frac{\Delta x_{2}}{\Delta t_{2}}-v$

$u = \frac{2811\,mi}{3\,h}-852\,\frac{mi}{h}$

$u = 85\,\frac{mi}{h}$

The rate of the wind is 85 miles per hour.