An aircraft flew 6 hours with the wind. The return trip took 7 hours against the wind. If the speed of the plane in still air is 276 miles per hour more than the speed of the wind, find the wind speed and the speed of the plane in still air.
The wind soeed was ______ mph.
i need help on this question
To solve this problem, we can use the concept of relative speed. Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".
According to the given information, the plane flew for 6 hours with the wind and took 7 hours against the wind.
When flying with the wind, the total speed (plane's speed + wind's speed) is equal to the distance traveled divided by the time taken:
6(p + w) = Distance
Similarly, when flying against the wind, the total speed (plane's speed - wind's speed) is equal to the distance traveled divided by the time taken:
7(p - w) = Distance
Since the distance traveled is the same in both cases (while flying with and against the wind), we have:
6(p + w) = 7(p - w)
Now, let's solve this equation to find the values of "p" (plane's speed in still air) and "w" (wind speed).
6p + 6w = 7p - 7w
Rearrange the equation:
6w + 7w = 7p - 6p
13w = p
Given that the speed of the plane in still air is 276 miles per hour more than the speed of the wind, we can write:
p = w + 276
Now, substitute the value of "p" obtained from the previous equation:
13w = w + 276
12w = 276
Divide both sides by 12:
w = 23
So, the wind speed is 23 mph.
To find the speed of the plane in still air, substitute the value of "w" back into the equation:
p = w + 276
p = 23 + 276
p = 299
Therefore, the speed of the plane in still air is 299 mph.