A plane makes a 240-mile trip against a head wind in 1 hour and 30 minutes and returns, with a tail wind of the same speed, in 1 hour. What is the speed of the wind?
A) 80 mph
B) 200 mph
C) 40 mph
D) 160 mph
p - w = 240 / 1.5
p + w = 240 / 1
adding equations ... 2 p = 400
solve for p , then substitute back to find w
1 hour = 60 minutes 240 + 30 m+ 1 hour = 330 is the speed
To determine the speed of the wind, we need to set up a system of equations using the given information.
Let's denote the speed of the plane as "p" and the speed of the wind as "w".
When the plane is flying against the headwind, the effective speed is reduced, so the total speed is (p - w).
When the plane is flying with the tailwind, the effective speed is increased, so the total speed is (p + w).
We know that the plane travels a distance of 240 miles in 1 hour and 30 minutes (or 1.5 hours) against the headwind, and the distance is the same when it returns with the tailwind in 1 hour. So we can set up the following equations:
240 = (p - w) * 1.5
240 = (p + w) * 1
Let's solve this system of equations to find the values of p and w.
First, divide both sides of the first equation by 1.5:
160 = p - w
Next, simplify the second equation:
240 = p + w
Now, we have a system of equations:
160 = p - w
240 = p + w
Add the two equations together:
400 = 2p
Divide both sides by 2:
200 = p
Now that we have the speed of the plane (p = 200), we can substitute it into one of the original equations to find the speed of the wind.
Using the second equation:
240 = 200 + w
240 - 200 = w
40 = w
So, the speed of the wind is 40 mph.
Therefore, the correct answer is C) 40 mph.