Question

A plane flies 440 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the vind is 25mph, find the speed of the plane in still air.

Answer 1

To find the speed of the plane in still air, set up equations representing the time it takes to fly with and against the wind. Simplify the equation and find that the speed of the plane in still air is 7.8 times the speed of the wind.

Step-by-step explanation:

To find the speed of the plane in still air, let's represent the speed of the plane as 'p' and the speed of the wind as 'w'. The plane flies 440 miles with the wind, so the time it takes to fly this distance can be represented as 440/(p+w). The plane also flies 340 miles against the wind, so the time it takes to fly this distance can be represented as 340/(p-w).

According to the given information, the speed of the wind is 25 mph. Setting up the equations:

440/(p+w) = 340/(p-w)

Simplifying the equation:

440(p-w) = 340(p+w)

Expanding:

440p - 440w = 340p + 340w

Combining like terms:

100p = 780w

Dividing both sides by 100w:

p = 7.8w

So, the speed of the plane in still air is 7.8 times the speed of the wind.