Question

at a maximum speed an airplane travels 2100 miles against the wind in 6 hours. Flying with the wind, the plane travel the same distance in 4 hours. what is the speed of the plane with no wind?

Answer 1

To find the speed of the plane with no wind, use the concept of relative velocity. Set up and solve equations using the effective speed of the plane against and with the wind. Substitute the value of the wind speed into either equation to find the speed of the plane with no wind.

Step-by-step explanation:

To find the speed of the plane with no wind, we can use the concept of relative velocity. Let's assume the speed of the wind is w and the speed of the plane is p.

Against the wind: The effective speed of the plane is p - w. Given that it travels 2100 miles in 6 hours, we have the equation (p - w) * 6 = 2100.

With the wind: The effective speed of the plane is p + w. Given that it travels the same distance in 4 hours, we have the equation (p + w) * 4 = 2100.

Solving these two equations simultaneously will give us the values of p and w. Since we're interested in the speed of the plane with no wind, we can substitute the value of w into either of the equations and solve for p.

Answer 2

Let x be the maximum speed of the plane and y be the speed of the wind

***Note: D = r*t or r = D/t***

x +y = 525mph |2100mi/4hr = 525mph

x -y = 350mph |2100mi/6hr = 350mph

2x = 875

x = 437.5mph, speed of plane. Wind speed is 87.5