The speed of the plane in still air = 585 mph
and the speed of the wind = 65 mph
What is speed?
"It is the distance covered per unit time."
What is the formula of speed?
"speed = distance/time"
For given question,
Let, the speed of the airplane in still air = x mph
and the speed of the wind = y mph
So, the speed of the airplane with the wind = (x + y) mph
and the speed of the airplane against the wind = (x - y) mph
Here, the distance (d) = 2600 miles
An airplane takes 4 hours to travel a distance of 2600 miles with the wind.
[tex]\Rightarrow x+y=\frac{2600}{4} \\\\\Rightarrow x+y=650~~~~~~~~~~.........................(i)[/tex]
The return trip takes 5 hours against the wind.
This means, an airplane takes 5 hours to travel a distance of 2600 miles against the wind.
[tex]\Rightarrow x-y=\frac{2600}{5}\\\\ \Rightarrow x-y=520~~~~~~~~~~............................(ii)[/tex]
From equation (ii),
x = 520 + y ........................(iii)
Substitute this value in equation (i),
⇒ (520 + y) + y = 650
⇒ 2y = 650 - 520
⇒ 2y = 130
⇒ y = 65 mph
Substitute the value of y in equation (iii),
⇒ x = 520 + y
⇒ x = 520 + 65
⇒ x = 585 mph
Therefore, the speed of the plane in still air = 585 mph
and the speed of the wind = 65 mph
Learn more about the speed here:
https://brainly.com/question/7359669
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