Flying with the wind, a pilot flew 600 mi between two cities in 4 h. The return trip against the wind took 5 h. Find the rate of the plane in calm air and the rate of the wind. Please show work. thanks
Distance (times) rate (times) time
Let p represent the speed of the plane in still air
Let w represent the speed of the wind
600= (p+w)(4)
600= (p-w)(5)
600 divided by 4= 150= p+w
600 divided by 5= 120= p-w
150+120= 270=2p
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divide 2 2
=135 =p
p+w= 150
135+w= 150
-135 -135
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w = 15
The speed of the plane in still air is 135 mph.
The speed of the wind is 15 mph.
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.