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?

The Miller Family used the sprinkler for 40 hours.

The Washington Family used the sprinkler for 30 hours.

Step-by-step 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

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

Step-by-step 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:

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

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

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^