Flying with wind, a plane flew 800 miles in 5 hrs. Flying against the wind, the plane flew the same distance in 8 hrs. Find the still air speed and wind speed.
If the plane's air speed is s, and the wind speed is w
800/(s+w) = 5
s+w = 160
800/(s-w) = 8
s-w = 100
2s=260
s=130
so, w=30
800/160 = 5
800/100 = 8
What's the 2s equation ??
To find the still air speed and wind speed, we can use the concept of relative speed.
Let's assume the still air speed of the plane is represented by "S" and the wind speed is represented by "W".
When the plane is flying with the wind, its effective speed increases. So, the speed of the plane with the wind is (S + W).
Similarly, when the plane is flying against the wind, its effective speed decreases. So, the speed of the plane against the wind is (S - W).
We are given that when flying with the wind, the plane covers a distance of 800 miles in 5 hours. This can be represented as:
Distance = Speed × Time
800 = (S + W) × 5
We are also given that when flying against the wind, the plane covers the same distance of 800 miles in 8 hours. This can be represented as:
Distance = Speed × Time
800 = (S - W) × 8
Now we have two equations:
1) 800 = 5(S + W)
2) 800 = 8(S - W)
We can solve these equations simultaneously to find the values of S (Still air speed) and W (Wind speed).