Answer: the speed of the plane with no wind is 500 miles per hour.
the speed of the wind is 100 miles per hour.
Explanation:
Let x represent the speed of the plane.
Let y represent the speed of the wind.
Traveling with the wind, a plane takes 2 1/2 = 2.5 hours to fly a distance of 1500 miles. The total speed would be x + y
Distance = speed × time
It means that
1500 = 2.5(x + y)
1500 = 2.5x + 2.5y - - - - - - - - - 1
The return trip of 1500 miles against the same wind speed, takes 3 hours. The total speed is x - y
It means that
1500 = 3(x - y)
1500 = 3x - 3y - - - - - - - - - - - - 2
Multiplying equation 1 by 3 and equation 2 by 2, it becomes
4500 = 7.5x + 7.5y
3000 = 7.5x - 7.5y
Adding both equations, it becomes
7500 = 15x
x = 7500 /15 = 500
Substituting x = 500 into equation 1, it becomes
1500 = 2.5 × 500 + 2.5y
1500 = 1250 + 2.5y
2.5y = 1500 - 1250 = 250
y = 250/2.5 = 100