Final answer:
To find the speed of the plane in still air and the speed of the wind, we set up a system of equations from the given travel times and distances. Solving the system, the speed of the plane in still air is 78 miles per hour, and the speed of the wind is 13 miles per hour.
Step-by-step explanation:
We are given a situation where an airplane travels to Cairo and back, with different travel times due to wind assistance and resistance. To find the speed of the airplane in still air and the speed of the wind, we need to set up two equations based on the information given. Let x represent the speed of the plane in still air, and y represent the speed of the wind.
For the trip to Cairo with the wind, the effective speed is x + y and the time taken is 10 hrs, leading to the equation:
(x + y) * 10 = 910
For the trip back against the wind, the effective speed is x - y and the time taken is 14 hrs, resulting in the equation:
(x - y) * 14 = 910
Solving this system of equations yields the values of x and y. First, we simplify the equations to:
x + y = 91
x - y = 65
By adding both equations, we get 2x = 156, so x = 78 miles per hour (speed of the plane in still air). To find y, substitute x into either equation. For example:
78 + y = 91
y = 91 - 78
y = 13 miles per hour (speed of the wind)