Togo flew his ultralight plane to a landing field 30 miles away. with the wind, the flight took three and a half hours. returning against the wind, the flight took 5 1/2 hours. find the rate of the plane in still air in the rate of the wind.

rate of the plane in still air is 7 mph

the rate of wind is 1.55 mph

Step-by-step 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

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )