A plane flies the first half of a 5600 km flight into the wind in 3.5 hours. The return trip, with the same wind, takes 2.5 hours. Find the speed of the wind and the speed of the plane in still air.
To solve this problem, let's denote the speed of the plane in still air as 'p' and the speed of the wind as 'w'.
We know that the time taken to fly the first half of the journey against the wind is 3.5 hours. This means that the plane's speed relative to the ground is p - w. Similarly, the time taken to return the same distance with the wind is 2.5 hours, which means the plane's speed relative to the ground is p + w.
Now, we can use the formula Distance = Speed × Time to create two equations and solve for p and w.
Equation 1:
Distance flown against the wind = Speed against the wind × Time against the wind
5600/2 = (p - w) × 3.5
Equation 2:
Distance flown with the wind = Speed with the wind × Time with the wind
5600/2 = (p + w) × 2.5
Simplifying both equations, we have:
2800 = 3.5p - 3.5w (equation 1)
2800 = 2.5p + 2.5w (equation 2)
Now, we can solve these two equations simultaneously. By multiplying equation 1 by 2 and equation 2 by 7 to eliminate w, we get:
5600 = 7p - 7w
5600 = 17.5p + 17.5w
Adding the two equations together, we have:
0 = 24.5p
Dividing both sides by 24.5, we find:
p = 0
From equation 1, we have:
2800 = - 3.5w
Solving for w, we find:
w = -800
Since speed cannot be negative, this result is not valid in the context of the problem. Therefore, there seems to be an inconsistency in the given information or conditions. Please double-check the values provided or the wording of the problem.
s = plane's speed
w = wind speed
2800/(s-w) = 3.5
2800/(s+w) = 2.5
3.5s - 3.5w = 2800
2.5s + 2.5w = 2800
s = 960
w = 160
2800/800 = 3.5
2800/1120 = 2.5