Im having a hard time trying to figure out how to do this problem:
A plane can fly 150 mph in calm air. Flying with the wind, the plane can fly 350 mi in the same amount of time it takes to fly 250 mi against the wind. Find the rate of the wind.
Let x = wind rate
Speed = distance/time, therefore
time = distance/speed
350/(150+x) = 250/(150-x)
Solve for x.
Thanks
To solve this problem, first, let's denote the rate of the wind as "w" (in mph).
When the plane is flying with the wind, its effective speed is increased by the rate of the wind. So the plane's speed with the wind is 150 + w mph.
When the plane is flying against the wind, its effective speed is decreased by the rate of the wind. So the plane's speed against the wind is 150 - w mph.
Let's now set up two equations based on the given information:
Equation 1: Distance traveled with the wind = 350 miles
Time taken with the wind = Distance / Speed = 350 / (150 + w)
Equation 2: Distance traveled against the wind = 250 miles
Time taken against the wind = Distance / Speed = 250 / (150 - w)
Since we are told that the time taken in both cases is the same, we can set these two equations equal to each other:
350 / (150 + w) = 250 / (150 - w)
To solve this equation for "w," we can cross-multiply to eliminate the denominators:
350(150 - w) = 250(150 + w)
Simplifying further:
52500 - 350w = 37500 + 250w
Now, let's solve for "w" by gathering like terms:
600w = 15000
Dividing both sides by 600:
w = 25
So, the rate of the wind is 25 mph.