Question

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.

Answer 1

Answer:

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: $18 = \frac{1}{3}(x+y)$

Return trip: $18 = \frac{3}{5}(x+y)$

We solve for x  and y

$18 = \frac{1}{3}(x+y)$

Multiply both sides by 3

54= x+ y

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

$18 = \frac{3}{5}(x+y)$

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

Answer 2

Dalia had an average airspeed of ⇒ 42 miles per hour.
The average wind speed was  ⇒ 12 miles per hour.