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.

Question

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

Answer 1

use 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

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

Answer 2

To solve this problem, we can use a system of equations. Let's denote the rate of the plane in calm air as 'p' and the rate of the wind as 'w'.

When the plane is flying with the wind, the effective speed is increased by the wind speed. So, the plane's speed is p + w. The distance covered is 360 miles, and the time taken is 2 hours. Therefore, we can write the equation:

(360 miles) = (p + w) * (2 hours) -- Equation 1

Similarly, when the plane is flying against the wind, the effective speed is decreased by the wind speed. So, the plane's speed is p - w. The distance covered is 300 miles, and the time taken is still 2 hours. Therefore, we can write the equation:

(300 miles) = (p - w) * (2 hours) -- Equation 2

Now, we have two equations in two variables. We can solve this system of equations to find the values of 'p' and 'w'.

First, let's simplify the equations by multiplying out the terms:

Equation 1: 360 miles = 2p hours + 2w hours
Equation 2: 300 miles = 2p hours - 2w hours

Next, let's isolate 'p' in Equation 1 by subtracting 2w from both sides:

360 miles - 2w hours = 2p hours -- Equation 3

Now, we can substitute Equation 3 into Equation 2:

300 miles = (360 miles - 2w) hours - 2w hours

Simplify:

300 miles = 360 miles - 4w hours

Rearrange the equation:

-60 miles = -4w hours

Divide both sides by -4:

15 miles = w hours -- Equation 4

Now, substitute the value of 'w' from Equation 4 into Equation 3:

360 miles - 2(15 miles) = 2p hours

Simplify:

360 miles - 30 miles = 2p hours

330 miles = 2p hours

Divide both sides by 2:

165 miles = p hours -- Equation 5

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.