Suppose a plane flying west a distance of 600 miles take 6 hours .The return trip take 5 hour . Find the airspeed of the plane and the effect wind resistance has on the plane?
The upwind speed is 100 mi/hr, and the downwind speed is 120 mi/hr. So, if the plane's speed is p and the wind speed is w (clearly, from the west),
p+w = 120
p-w = 100
To find the airspeed of the plane and the effect of wind resistance, we can set up a system of equations.
Let's assume that the airspeed of the plane is represented by "p" and the speed of the wind is represented by "w." The actual ground speed of the plane against the wind is then (p - w), and the actual ground speed of the plane with the wind is (p + w).
We are given that the plane flies west a distance of 600 miles in 6 hours, so we can set up the following equation:
(p - w) * 6 = 600
Similarly, for the return trip, where the plane flies east, we are given that the plane takes 5 hours. Therefore, the equation for the return trip is:
(p + w) * 5 = 600
Now, we can simplify and solve this system of equations. Let's start by solving the first equation for p:
p - w = 600/6
p - w = 100
Similarly, we solve the second equation for p:
p + w = 600/5
p + w = 120
Now, we have two equations:
p - w = 100
p + w = 120
We can add these equations together to eliminate the variable "w":
2p = 220
p = 220/2
p = 110
So, the airspeed of the plane is 110 miles per hour.
To find the effect of wind resistance, we can substitute the value of p back into one of the original equations. Let's use the first equation:
(110 - w) * 6 = 600
Simplifying, we get:
660 - 6w = 600
Subtracting 660 from both sides:
-6w = 600 - 660
-6w = -60
Dividing by -6:
w = -60/-6
w = 10
Therefore, the speed of the wind is 10 miles per hour. The negative sign indicates that the wind is blowing in the opposite direction of the plane's motion. In this case, the wind resistance subtracts 10 miles per hour from the plane's airspeed.