A flight from a to B is against the wind and takes five hours return flight with wind takes 4.5 hours of the wind speed is 50 mph find the speed of the plane in still air
since distance = speed * time,
(s-50)(5) = (s+50)(4.5)
That's some fast plane!
To find the speed of the plane in still air, we need to apply the concept of relative speed.
Let's assume the speed of the plane in still air is "P" mph.
When the plane flies against the wind, the effective speed is reduced. In this case, the wind speed is 50 mph, so the effective speed of the plane against the wind would be (P - 50) mph.
We are given that the flight from A to B, against the wind, takes 5 hours. So we can calculate the distance between A and B using the formula: Distance = Speed × Time. Therefore, the distance from A to B would be (P - 50) × 5.
On the return flight, the plane flies with the wind, which increases its effective speed. The effective speed of the plane with the wind would be (P + 50) mph.
We are told that the return flight takes 4.5 hours. Using the formula Distance = Speed × Time, the distance from B to A would be (P + 50) × 4.5.
Since both flights cover the same distance (from A to B and from B to A), we can set up the equation:
(P - 50) × 5 = (P + 50) × 4.5
Now, we can solve this equation to find the value of P, which represents the speed of the plane in still air.
To solve for P, first expand both sides of the equation:
5P - 250 = 4.5P + 450
Now, bring all the P terms to one side of the equation and all the constant terms to the other side:
5P - 4.5P = 450 + 250
0.5P = 700
Finally, divide both sides of the equation by 0.5:
P = 700 / 0.5
P = 1400
Therefore, the speed of the plane in still air is 1400 mph.