Question

The Bailey family and the Howard family each used their sprinklers last summer. The water output rate for the Bailey family's sprinkler was 20L per hour. The water output rate for the Howard family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1625. How long was each sprinkler used?

Answer 1

Answer:

Running time of Bailey's family sprinkler = x = 20 hrs

Running time of Howard's family sprinkler = y = 35 hrs

Step-by-step explanation:

We will make equations of time and flow of each family's sprinkler.

1. Time equation will be:

Let x is the time of Bailey's family sprinkler

Let y is the time of Howard Family Sprinker

Thus equation from the given information is both sprinklers ran for 55 hours.

$x+y=55$                           (eq:1)

2. Flow of water equation will be derived from the fact that if we multiply the flow of one sprinkler with its time it will give the total flow of water

thus: Flow of Bailey's family sprinkler = $x*20$

and Flow of Bailey's family sprinkler = $y*35$

Total flow is given = 1625

Therefor adding the two equations will give total flow equation

$(x*20) + (y*35) = 1625$  

$20x+35y=1625$                    (eq:2)

Now we have two equations and two variables x and y and we will use the substitution method to solve them.

Using equation one

$x+y=55$

$x=55-y$

Using value of x in second equation

$20x +35y = 1625$

Substituting value of x

$20(55-y)) + 35y = 1625\\1100-20y+35y=1625\\1100+35y-20y=1625\\15y=1625-1100\\15y=525\\y=525/15\\y=35$

Now putting the value of y in equation # 1

$x+y=55\\x+35=55\\x=55-35\\x=20$

Thus the answers are:

Running time of Bailey's family sprinkler = x = 20 hrs

Running time of Howard's family sprinkler = y = 35 hrs

Answer 2

Answer:

The number of hours the Bailey family's sprinkler was used is 20 hours

The number of hours the Howard family's sprinkler was used is 35 hours

Step-by-step explanation:

Let x represent the number of hours the Bailey family's sprinkler was used.

Total number of hours worked is 55 hours

The number of hours the Howard family's sprinkler was used is 55-x

Given;

The water output rate for the Bailey family's sprinkler is 20L per hour.

The water output rate for the Howard family's sprinkler is 35L per hour.

Total water output is 1625L

So,

20(x) + 35(55-x) = 1625

20x -35x + 35(55) = 1625

-15x = 1625 - 1925

-15x = -300

x = -300/(-15)

x = 20

And,

55-x = 55-20 = 35

Therefore,

The number of hours the Bailey family's sprinkler was used is 20 hours

The number of hours the Howard family's sprinkler was used is 35 hours