Flying to Seoul with a tailwind a plane averaged 343 mph. On the return trip the plane only averaged 307 mph while flying back into the same wind. Find the speed of the plane in still air and the speed of the wind.
To find the speed of the plane in still air and the speed of the wind, we can use the concept of relative motion and the formula:
Speed of the Plane in Still Air = (Speed with Tailwind + Speed against Headwind) / 2
Speed of the Wind = (Speed with Tailwind - Speed against Headwind) / 2
Let's denote the speed of the plane in still air as "P" and the speed of the wind as "W".
Given that the plane averaged 343 mph with a tailwind, we can write the equation:
P + W = 343 ---- (1)
And, on the return trip, the average speed was 307 mph against the same wind:
P - W = 307 ---- (2)
To solve these equations simultaneously, we can add equations (1) and (2):
(P + W) + (P - W) = 343 + 307
Simplifying, we get:
2P = 650
Dividing both sides by 2, we find:
P = 325
Now that we know the speed of the plane in still air is 325 mph, we can substitute this value back into one of the original equations, say equation (1):
325 + W = 343
Subtracting 325 from both sides, we get:
W = 343 - 325
Simplifying, we find:
W = 18
Therefore, the speed of the plane in still air is 325 mph and the speed of the wind is 18 mph.