A Boeing 747 flies 2420 miles with the wind. In the same amount of time, it can fly 2140 miles against the wind. The cruising speed ( in still air) is 570 mph. Find the speed of the wind.
time with the wind = 2420/(570+x)
time against the wind = 2140/(570-x)
but these two times are equal
2420/(570+x) = 2140/(570-x)
1219800 + 2140x = 1379400 - 2420x
4560x = 159600
x = 35
the speed of the wind is 35 mph
To find the speed of the wind, we can use the concept of relative speed.
Let's assume that the speed of the wind is 'w' mph.
When the plane is flying with the wind, the total effective speed would be the sum of the plane's speed in still air and the speed of the wind. So the effective speed is (570 + w) mph.
Similarly, when the plane is flying against the wind, the total effective speed would be the difference between the plane's speed in still air and the speed of the wind. So the effective speed is (570 - w) mph.
We are given that the plane flies 2420 miles with the wind and 2140 miles against the wind in the same amount of time.
We know that Speed = Distance / Time.
Hence, the time taken to fly 2420 miles with the wind is 2420 / (570 + w) hours.
The time taken to fly 2140 miles against the wind is 2140 / (570 - w) hours.
Since both these times are equal, we can equate the two equations:
2420 / (570 + w) = 2140 / (570 - w).
Now, we can solve this equation to find the value of 'w', which represents the speed of the wind.
Cross multiplying, we get:
2420 * (570 - w) = 2140 * (570 + w).
Expanding this equation:
1379400 - 2420w = 1218800 + 2140w.
Combine the variables:
4560w = 160600.
Divide both sides by 4560:
w = 160600 / 4560 ≈ 35.21 mph.
Therefore, the speed of the wind is approximately 35.21 mph.