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.
I am so lost I don't even know how to set up the equations! Please help!
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.
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