Question

A plane traveled 4575 miles with the wind in 7.5 hours and 4275 miles against the wind in the same amount of time. Find the speed of the plane in still air and the
speed of the wind.
The speed of the plane in still air is mph. (Simplify your answer.)
The speed of the wind is mph. (Simplify your answer.)

Answer 1

Answer:

The speed of the plane in still air is 590 mph

The speed of the wind is 20 mph

Step-by-step explanation:

Let's call:

x = Speed of the plane in still air

y = Speed of the wind

The plane traveled d=4575 miles with the wind in t=7.5 h. The speed calculated with this data corresponds to the sum of the speed of the plane and the speed of the wind, thus:

$\displaystyle x+y=\frac{4575}{7.5}=610$

x + y = 610        [1]

The plane traveled 4275 miles in 7.5 hours against the wind, thus the speed calculated is x - y:

$\displaystyle x-y=\frac{4275}{7.5}=570$

x - y = 570        [2]

Adding [1] and [2]:

2x = 610 + 570 = 1180

x = 1180 / 2 = 590

From [1]:

y = 610 - 590 = 20

The speed of the plane in still air is 590 mph

The speed of the wind is 20 mph