Answer:rate of the plane in still air is 7 mph
the rate of wind is 1.55 mph
Explanation:
Let x represent the rate of the plane in still air.
Let y represent the rate of wind.
Togo flew his ultralight plane to a Landing field 30 miles away. With the wind, the flight took three and a half hours. This means that total speed = (x + y) mph
Distance = speed × time
Therefore
30 = 3.5(x + y)
30 = 3.5x + 3.5y - - - - - - - - - 1
Returning against the wind, the flight took 5 1/2 hours. This means that the total speed would be
(x - y) mph
Therefore,
30 = 5.5(x - y)
30 = 5.5x - 5.5y - - - - - - - - - -2
Multiplying equation 1 by 5.5 and equation 2 by 3.5, it becomes
165 = 19.25x + 19.25y
105 = 19.25x - 19.25y
Adding both equations, it becomes
270 = 38.5x
x = 270/38.5
x = 7 miles per hour
30 = 5.5 × 7 - 5.5y
30 = 38.5 - 5.5y
5.5y = 38.5 - 30 = 8.5
y = 8.5/5.5 = 1.55 miles per hour