an aircraft flew 2 hours with the wind. the return trip took 3 hours against the wind. if the speed of the plane in still air is 140 miles per hour more than the speed of the wind, find the wind speed and the speed of the plane in still air
v = 140 + w
(140+2w)2 = (140 +w -w )3 = 420
280 + 4 w = 420 etc
So what is the speed of the plane and the wind speed? This didn't help very much simplify it plz.
I said 280 + 4 w = 420
so
4 w = 140
w = 35 mph wind speed
now go back and get v
what is v
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".
When the aircraft flies with the wind, its effective speed is increased by the speed of the wind. So the speed with the wind is (p + w) miles per hour. Since it took 2 hours to fly with the wind, the distance traveled is then 2 * (p + w).
On the return trip against the wind, the effective speed of the aircraft is decreased by the speed of the wind. So the speed against the wind is (p - w) miles per hour. Since it took 3 hours to fly against the wind, the distance traveled is then 3 * (p - w).
The distance traveled with the wind is the same as the distance traveled against the wind. Therefore, we can set up the following equation:
2 * (p + w) = 3 * (p - w)
Now let's solve for "p" and "w":
2p + 2w = 3p - 3w (Distribute)
2p - 3p = 3w - 2w (Combine like terms)
-w = w
Since -w = w, this can only be true if w = 0. This means there is no wind.
However, the problem statement says that the speed of the plane in still air is 140 miles per hour more than the speed of the wind. Therefore, we can conclude that there must be a mistake in the problem statement or given information, as the equation provided does not have a valid solution.
To find the wind speed and the speed of the plane in still air, we would need additional information or a corrected problem statement.