Question

At maximum speed, an airplane travels 2,400 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours. Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?

Answer 1

Answer: The speed of the plane with no wind is 440 miles per hour.

Step-by-step explanation:

Let the maximum speed of the plane be 'x'.

Let the maximum speed of the wind be 'y'.

Since we have given that an airplane travels 2400 miles against the wind in 6 hours.

As we know that

Downstream is given by

$x+y=\dfrac{2400}{6}=400--------------(1)$

Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.

As we know tha t

Upstream is given by

$x-y=\dfrac{2400}{5}=480-------------------(2)$

We just need to find the speed of the plane with no wind.

Using the elimination method,

$x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440$

Hence, the speed of the plane with no wind is 440 miles per hour.

Answer 2

X - y  = 2400/6 = 400        where x = speed of plane and y = speed of wind.

x + y =  2400/5 = 480          - flying with the wind

adding the 2 equations 
2x = 880
x = 440

Speed of the plane with no wind = 440 mph