Dalia flies an ultralight plane with a tailwind to a nearby town in 1/3 of an hour. on the return trip, she travels the same distance in 3/5 of an hour. what is the average rate of speed of the wind and the average rate of speed of the plane?

initial trip:
return trip:
let x be the average airspeed of the plane.
let y be the average wind speed.
initial trip: 18 = (x + y)
return trip: 18 = (x – y)
dalia had an average airspeed of miles per hour.
the average wind speed was miles per hour.

the average airspeed of the plane = 42 miles per hour

the average wind speed = 12 miles per hour

Step-by-step explanation:

Let x be the average airspeed of the plane.

Let y be the average wind speed.

Distance =time * speed

Initial trip:

Return trip:

We solve for x  and y

Multiply both sides by 3

54= x+ y

y= 54- x ------------> equation 1

Multiply both side by 5

90 = 3(x-y)

90= 3x- 3y ------------------> equation 2

Plug in y=54-x in second equation

90= 3x- 3(54-x)

90 = 3x - 162 + 3x

90 = -162 + 6x

Add 162 on both sides

252= 6x

Divide both sides by 6

So x= 42

y= 54- x

Plug in 42 for x

y= 54 - 42= 12

the average airspeed of the plane = 42 miles per hour

the average wind speed = 12 miles per hour

its 4 because 2 times 2 is 4, if you double the number two you get four