Question

A plane traveling with the wind travels 900 miles in 5 hours. the return trip is against the wind and takes 9 hours. find the rate of the plane in still air and the rate of the wind.

Answer 1

Using the relation between velocity, distance and time, it is found that:

• The rate of the plane in still air is of 140 mph.

• The rate of the wind is of 40 mph.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

$v = \frac{d}{t}$

A plane traveling with the wind travels 900 miles in 5 hours, hence:

$v_a + v_w = \frac{900}{5}$

$v_a + v_w = 180$

The return trip is against the wind and takes 9 hours, hence:

$v_a - v_w = \frac{900}{9}$

$v_a - v_w = 100$

From the first equation, we have that:

$v_w = 180 - v_a{/tex]

Replacing on the second:

[tex]v_a - v_w = 100$

$v_a - 180 + v_a = 100$

$2v_a = 280$

$v_a = 140$

[tex]v_w = 180 - 140 = 40{/tex]

Hence:

• The rate of the plane in still air is of 140 mph.

• The rate of the wind is of 40 mph.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569