With a tail wind, a light plane can fly 720 km in 2h. Going against the wind, the plane can fly the same distance in 3 h. What are the wind speed and the air speed of the plane?
p + w = 720 / 2
p - w = 720 / 3
add the equations to find p
substitute back to find w
To find the wind speed and the airspeed of the plane, we can set up a system of equations using the given information.
Let's assume that the airspeed of the plane is represented by "p" (in km/h) and the wind speed is represented by "w" (in km/h).
Now, let's consider the situation when the plane is flying with a tailwind. In this case, the effective speed of the plane is the sum of its airspeed and the wind speed (p + w). We are given that the plane can fly 720 km in 2 hours, so we can set up the equation:
(p + w) * 2 = 720
Next, let's consider the situation when the plane is flying against the wind. In this case, the effective speed of the plane is the difference between its airspeed and the wind speed (p - w). We are given that the plane can fly the same distance of 720 km, but it takes 3 hours. So we can set up another equation:
(p - w) * 3 = 720
Now, we have a system of equations:
2(p + w) = 720
3(p - w) = 720
To solve this system of equations, we can use the method of substitution or elimination. I'll use the method of substitution here:
From the first equation, we can simplify it to get:
2p + 2w = 720
Let's solve this equation for p:
2p = 720 - 2w
p = (720 - 2w) / 2
p = 360 - w
Now, we can substitute this expression for p in the second equation:
3((360 - w) - w) = 720
Let's simplify and solve this equation for w:
3(360 - 2w) = 720
1080 - 6w = 720
-6w = 720 - 1080
-6w = -360
w = -360 / -6
w = 60
So, the wind speed is 60 km/h.
To find the airspeed, we can substitute the value of w into one of the equations. Let's use the first equation:
2(p + 60) = 720
Solving this equation for p:
2p + 120 = 720
2p = 720 - 120
2p = 600
p = 600 / 2
p = 300
Therefore, the airspeed of the plane is 300 km/h.