To find the rate of the plane in calm air and the rate of the wind, we can use the following formula:
Rate of the plane in calm air = (Rate with the wind + Rate against the wind) / 2
And,
Rate of the wind = Rate with the wind - Rate of the plane in calm air
Let's solve the problem step by step:
Step 1: Determine the distance and time for each leg of the journey.
Flying with the wind:
Distance = 600 miles
Time = 4 hours
Against the wind:
Distance = 600 miles
Time = 5 hours
Step 2: Calculate the rates with the wind and against the wind.
Rate with the wind = Distance / Time
Rate against the wind = Distance / Time
For the trip with the wind:
Rate with the wind = 600 miles / 4 hours = 150 mph
For the trip against the wind:
Rate against the wind = 600 miles / 5 hours = 120 mph
Step 3: Calculate the rate of the plane in calm air.
Rate of the plane in calm air = (Rate with the wind + Rate against the wind) / 2
Rate of the plane in calm air = (150 mph + 120 mph) / 2
Rate of the plane in calm air = 270 mph / 2
Rate of the plane in calm air = 135 mph
Step 4: Calculate the rate of the wind.
Rate of the wind = Rate with the wind - Rate of the plane in calm air
Rate of the wind = 150 mph - 135 mph
Rate of the wind = 15 mph
So, the rate of the plane in calm air is 135 mph, and the rate of the wind is 15 mph.