Final answer:
To find the average rate of speed of the wind and the average rate of speed of the plane, we can use the concept of relative velocity. Let's assume the average airspeed of the plane as x km/h and the average wind speed as y km/h. By setting up and solving equations, we can find the values of x and y.
Step-by-step explanation:
To find the average rate of speed of the wind and the average rate of speed of the plane, we can use the concept of relative velocity.
Let's assume the average airspeed of the plane as x km/h and the average wind speed as y km/h.
On the initial trip with the tailwind, the plane covers a certain distance in 1/3 of an hour. So, the relative speed of the plane and wind is (x + y) km/h.
Similarly, on the return trip, the plane covers the same distance in 3/5 of an hour. So, the relative speed of the plane and wind is (x - y) km/h.
We can set up the following equations:
(x + y) = distance / (1/3) and (x - y) = distance / (3/5)
Solving these equations will give us the values of x and y, which represent the average rate of speed of the plane and the wind, respectively.