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

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?