A plane flies from city x to city y against the wind in 8 hours and flies back from city y to city x with the wind in 5 hours. If the speed of the wind is 650 mph, find the wind speed in mph?
To find the wind speed, we need to set up a system of equations based on the given information.
Let's assume that the speed of the plane, without the influence of the wind, is represented by "p" (in mph) and the speed of the wind is represented by "w" (in mph). The equation for the plane's speed while flying against the wind can then be written as:
p - w = (distance between city x and city y) / (time taken to fly against the wind)
Similarly, the equation for the plane's speed while flying with the wind can be written as:
p + w = (distance between city y and city x) / (time taken to fly with the wind)
From the given information, we know that the time taken to fly against the wind is 8 hours and the time taken to fly with the wind is 5 hours. We also know that the distance traveled in both directions is the same. Therefore, we can assume that the distance between city x and city y is equal to the distance between city y and city x.
Let's assign a variable "d" to represent the distance between city x and city y.
Now we can rewrite the two equations as follows:
p - w = d / 8 ----(1)
p + w = d / 5 ----(2)
To find the wind speed, we need to eliminate the variable "p" from these equations. We can do this by adding equation (1) and equation (2) together, which will eliminate the "p" term:
(p - w) + (p + w) = d / 8 + d / 5
Simplifying this equation will give us:
2p = (5d + 8d) / (8*5)
2p = 13d / 40
p = (13d / 40) * (1/2)
p = (13d / 80)
Now, we can substitute the value of "p" in any of the original equations (1) or (2) to solve for "w". Let's use equation (1) since it is simpler:
(13d / 80) - w = d / 8
To simplify this equation, we need to get rid of the denominators:
Multiply both sides of the equation by 80 to eliminate the fraction:
13d - 80w = 10d
Rearranging the terms, we have:
13d - 10d = 80w
3d = 80w
Finally, divide both sides of the equation by 80 to isolate "w":
w = (3d / 80)
Since the question doesn't provide the specific distance between city x and city y, we cannot determine the exact wind speed. However, we can conclude that the wind speed is equal to (3d / 80) mph based on the given information.
That is some wind!!!
I think you have a typo and meant that the plane's speed is 650 mph.
however, taking it as is:
let the plane's speed be x mph
from city x to city y: distance = 8(x-650)
from city y to city x: distance = 5(x+650)
8(x-650) = 5(x+650)
solve for x , you will get a speed of 2817 mph
Make the necessary changes.