A plane that can fly 275 mph in still air for 3 hours against a wind and for 2 hours with the same wind. The total distance it covers is 1300 miles. Find the rate of the wind.
Let w be the rate of the wind.
Use d = r * t (distance = rate * time).
For "against the wind," you must subtract w. The opposite goes for "with the wind."
To find the rate of the wind, we can set up a system of equations based on the given information.
Let's assume that the speed of the plane in still air is represented by the variable "p" and the rate of the wind is represented by the variable "w".
When flying against the wind, the effective speed of the plane is reduced by the wind's speed. So, the speed of the plane against the wind is p - w.
When flying with the wind, the effective speed of the plane is increased by the wind's speed. So, the speed of the plane with the wind is p + w.
Now, we can use the formula: Distance = Speed × Time
For the first scenario (against the wind):
Distance = (p - w) × 3
For the second scenario (with the wind):
Distance = (p + w) × 2
Given that the total distance covered is 1300 miles, we can write the equation:
(p - w) × 3 + (p + w) × 2 = 1300
Let's simplify this equation step by step:
3p - 3w + 2p + 2w = 1300
5p - w = 1300
Now, we have one equation with two variables. However, we can solve this equation if we have another equation involving the variables p and w.
Since the plane's speed in still air is given as 275 mph, we have the equation p = 275.
Substituting the value of p into our equation:
5(275) - w = 1300
1375 - w = 1300
Now, solve for w:
w = 1375 - 1300
w = 75
Therefore, the rate of the wind is 75 mph.