Question

The Miller family and the Washington family each used their sprinklers last summer. The water output rate for the Miller family's sprinkler was 30 l per hour. The water output rate for the Washington family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 70 hours, resulting in a total water output of 1650 L

. How long was each sprinkler used?

Answer 1

The Miller Family used the sprinkler for 40 hours.

The Washington Family used the sprinkler for 30 hours.

Explanation:

First write an equation.

M = Miller Family's Output Rate

W = Washington Family's Output Rate

30M + 15W = 1650

M + W = 70

Using simultaneous equations:

1) Make one of the coefficients the same value.

We will make both W's 15.

Multiply the second equation by 15.

15M + 15W = 1050

2) Subtract the equations to remove the coefficient.

(30M + 15W = 1650) - (15M + 15W = 1050)

(30M + 15W) - (15M + 15W) = 1650 - 1050

15M = 600

3) Divide to find the value of 1 M

15M = 600

M = 600/15

M = 40

4) Substitute M into either equation to find the value of W.

30M + 15W = 1650

30(40) + 15W = 1650

1200 + 15W = 1650

15W = 1650 - 1200

15W = 450

W = 450/15

W = 30

M + W = 70

40 + W = 70

W = 70 - 40

W = 30

Answer 2

Miller family's sprinkler was used for 40 hours and Washington family's sprinkler was used for 30 hours.

Explanation:

Set up a system of equations.

Let be "m" the time Miller family's sprinkler was used and "w" the time Washington family's sprinkler was used.

Then:

`\left \{ {{m+w=70} \atop {30m+15w= 1,650}} \right.`

You can use the Elimination method. Multiply the first equation by -30, then add both equations and solve for "w":

`\left \{ {{-30m-30w=-2,100} \atop {30m+15w= 1,650}} \right.\\.................................\\-15w=-450\\w=30`

Substitute w=30 into an original equation and solve for "m":

`m+30=70\\m=70-30\\m=40`