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

To solve this problem, set up a system of equations where x represents the average airspeed of the plane and y represents the average wind speed. Solve the system to find the values of x and y.

Step-by-step explanation:

To solve this problem, we can set up a system of equations:

Let x be the average airspeed of the plane.

Let y be the average wind speed.

For the initial trip, the plane is flying with a tailwind, so the equation would be x + y = 18 (in miles per hour).

For the return trip, the plane is flying against the wind, so the equation would be x - y = 18.

Solving this system of equations will give us the values of x and y, which represent the average rate of speed of the plane and the wind, respectively.

After solving the system of equations, we find that the average airspeed of the plane (x) is 9 miles per hour and the average wind speed (y) is 9 miles per hour.

Answer 2

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 = (1)/(3)(x+y)`

Return trip:
`18 = (3)/(5)(x+y)`

We solve for x and y

`18 = (1)/(3)(x+y)`

Multiply both sides by 3

54= x+ y

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

`18 = (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