An airplane flying into a headwind travels the 2800 mile flying distance between two cities in 4 hours and 40 minutes. On the return flight, the same distance is traveled in 4 hours. Find the air speed of the plane and the speed of the wind assuming that neither changes. Find the plane and wind speed.
I am so lost I don't even know how to set up the equations! Please help!
W=wind speed
A=air speed
Equation are set up using
Speed*Time = distance,
or
Distance/Speed = Time
2800/(A-W)=4 2/3 ...(1)
2800/(A+W)=4 ...(2)
Solve system of equations for A and W.
u57r65
To solve this problem, we need to set up two equations using the given information. Let's assume the airspeed of the plane is represented by "p" and the speed of the wind is represented by "w."
Equation 1: (Airplane's speed with the wind) = (Airplane's airspeed) + (Wind's speed)
Equation 2: (Airplane's speed against the wind) = (Airplane's airspeed) - (Wind's speed)
From the information given, we have two equations:
Equation 1: 2800 = (p + w) * 4 hours and 40 minutes
Equation 2: 2800 = (p - w) * 4 hours
First, let's convert the 4 hours and 40 minutes to hours. We know that 1 hour is equal to 60 minutes, so 40 minutes is equal to 40/60 = 2/3 hours. Therefore, 4 hours and 40 minutes is equal to 4 + 2/3 = 14/3 hours.
Now, we can rewrite the equations as:
Equation 1: 2800 = (p + w) * (14/3)
Equation 2: 2800 = (p - w) * 4
To solve these equations simultaneously, we can use a method called substitution. First, isolate one variable in terms of the other in one of the equations. Let's isolate "p" in terms of "w" in Equation 1:
Equation 1: 2800 = (p + w) * (14/3)
2800 = (14/3)p + (14/3)w
Multiply both sides by 3:
8400 = 14p + 14w
Simplify:
8400 - 14w = 14p
Divide both sides by 14:
600 - w = p
Now, substitute this value of "p" into Equation 2:
2800 = (600 - w - w) * 4
2800 = (600 - 2w) * 4
2800 = 2400 - 8w
400 = -8w
w = -400/8
w = -50
Now, substitute this value of "w" back into Equation 1 to find "p":
2800 = (p + (-50)) * (14/3)
2800 = (14/3)p - (50*14/3)
2800 + (700/3) = (14/3)p
To simplify the equation, we need to find a common denominator for 3 and 14. LCM(3, 14) = 42.
Multiply both sides by 42/42 to clear the fraction:
(2800 * 42/3) + (700/3) = 14p
(2800 * 14) + 700 = 42p
39200 + 700 = 42p
39900 = 42p
p = 39900/42
p = 950
So, the airspeed of the plane is 950 mph and the speed of the wind is 50 mph.
To summarize:
Airspeed of the plane = 950 mph
Speed of the wind = 50 mph