To determine the speed of the plane and the speed of the wind, we need to set up a system of equations using the given information.
Let's assume that the speed of the plane is represented by "p" (in miles per hour) and the speed of the wind is represented by "w" (in miles per hour).
When the plane is flying with the wind, the effective speed of the plane will be the sum of its actual speed and the speed of the wind. Therefore, the equation for the distance covered with the wind can be written as:
c = (p + w) * a.....(1)
Similarly, when the plane is flying against the wind, the effective speed of the plane will be the difference between its actual speed and the speed of the wind. Hence, the equation for the return trip against the wind can be written as:
c = (p - w) * b.....(2)
We are given that a = 3 hours, b = 4.5 hours, and c = 720 miles.
Substituting the given values into equations (1) and (2), we get:
720 = (p + w) * 3.....(3)
720 = (p - w) * 4.5.....(4)
Now we have a system of two equations with two variables. We can solve this system to find the values of p and w.
Divide equation (3) by 3:
240 = p + w.....(5)
Divide equation (4) by 4.5:
160 = p - w.....(6)
Now we have a system of two equations:
240 = p + w.....(5)
160 = p - w.....(6)
To solve this system, we can add equations (5) and (6):
240 + 160 = (p + p) + (w - w)
400 = 2p
Divide both sides of the equation by 2:
200 = p
Therefore, the speed of the plane is 200 miles per hour.
To find the speed of the wind, we will substitute the value of p back into equation (5):
240 = 200 + w
Subtract 200 from both sides:
40 = w
Therefore, the speed of the wind is 40 miles per hour.
So, the plane's speed is 200 mph and the speed of the wind is 40 mph.