Flying with the wind, a small plane flew 360 miles in 2hours. Against the wind, the plane could fly only 300 miles in the same amount of time. Find the rate of the plane in calm air and the rate of the wind.

I cant figure out how to solve this. Please help me

use the variables p for plane and w for wind and the equations:

(p+w)x 2hours = 360 miles
(p-w)x 2hours = 300 miles
divide by 2

p+w=180
p-w=150
combine the two equations so w cancels out

2p = 330
divide by 2 to get the speed of the plane.

p=165
put the plane back into the equation to get the rate of the wind

165+w = 180
w = 15m/h

To solve this problem, we can use the formula:

Distance = Rate × Time

Let's denote the rate of the plane in calm air as 'p' (in miles per hour) and the rate of the wind as 'w' (in miles per hour).

When the plane is flying with the wind, its effective speed is increased by the speed of the wind. So, the speed of the plane with the wind is 'p + w'. Given that the plane flies 360 miles in 2 hours, we can write the equation:

360 = (p + w) × 2 -----> Equation 1

Similarly, when the plane is flying against the wind, its effective speed is decreased by the speed of the wind. So, the speed of the plane against the wind is 'p - w'. Given that the plane flies 300 miles in 2 hours, we can write the equation:

300 = (p - w) × 2 -----> Equation 2

Now, we have a system of two equations with two unknowns. We can solve this system using various methods, such as substitution or elimination.

Let's solve the system by using the elimination method. We will subtract Equation 2 from Equation 1 to eliminate 'w':

360 - 300 = (p + w) × 2 - (p - w) × 2
60 = 2p + 2w - 2p + 2w
60 = 4w
w = 60/4
w = 15

Now that we know the rate of the wind (w = 15), we can substitute this value back into either Equation 1 or Equation 2 to find the rate of the plane in calm air (p).

Let's substitute w = 15 into Equation 1:

360 = (p + 15) × 2
360/2 = p + 15
180 = p + 15
p = 180 - 15
p = 165

Therefore, the rate of the plane in calm air is 165 miles per hour, and the rate of the wind is 15 miles per hour.

I hope this explanation helps you understand how to solve the problem!