# An airplane takes 7 hours to travel a distance of 4707km against the wind. The return trip takes 6 hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?

Jul 17, 2018

The speed of the airplane is $= 728.5 k m {h}^{-} 1$. The speed of the wind is $= 56.0 k m {h}^{-} 1$

#### Explanation:

Let the speed of the airplane in still air be $= {v}_{a} k m {h}^{-} 2$

Let the speed of the wind be $= {v}_{w} k m {h}^{-} 2$

Thefore,

Then, the on going speed is

${v}_{a} - {v}_{w} = \frac{4707}{7}$...................$\left(1\right)$

And the return journey is

${v}_{a} + {v}_{w} = \frac{4707}{6}$..................$\left(2\right)$

Solving equations $\left(1\right)$ and $\left(2\right)$

$2 {v}_{a} = \frac{4707}{7} + \frac{4707}{6} = 4707 \left(\frac{1}{7} + \frac{1}{6}\right)$

${v}_{a} = 728.5 k m {h}^{-} 1$

The speed of the airplane is $= 728.5 k m {h}^{-} 1$

And

$2 {v}_{w} = \frac{4707}{6} - \frac{4707}{7} = 4707 \left(\frac{1}{6} - \frac{1}{7}\right)$

${v}_{w} = 56.0 k m {h}^{-} 1$

The speed of the wind is $= 56.0 k m {h}^{-} 1$