Question

The Scott family and the Rogers family each used their sprinklers last summer. The water output rate for the Scott family's sprinkler was 37L per hour. The water output rate for the Rogers family's sprinkler was 20L per hour. The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 1175L . How long was each sprinkler used? How much used by the Scott family and how much used for the Rogers family?

Answer 1

Let Scott hours= S
Let Rogers hours = R

then S + R = 40

the amount of water times the hours they ran the sprinklers will give the total output of water:

S x 35 + R x 25 = 1425, or
35S + 25R = 1425

so now you have two equations:

S + R = 40 and
35S + 25R = 1425

Answer 2

Solve the first equation for S:
S = 40 - R
then substitute it into the second equation:
35(40 - R) + 25R = 1425

When you solve this equation for R, you will know how many hours the Rogers used their water. Once you know that, you can find out how many hours the Scotts used their water.

To find out how much water each family used, multiply the number of hours they ran their water times the number of Ls each family used.

Answer 3

You still there?

Answer 4

yep

Answer 5

Im going to try to work it AHHHHHHHH

Answer 6

There's something wrong with the amounts given. I'm coming up with Scotts using 42.5 hours of water and Rogers using -2.5 hours of water, but it isn't possible to use a negative amount of water!

Answer 7

Should be 20 L not 25 and 1175 total.

Answer 8

That makes sense now. Scott = 25 and Rogers = 15

Answer 9

Had to edit the entire thing my apologies

Answer 10

no worries---it happens to the best of us!

Answer 11

so your 2 equations would be
S + R = 40
35S + 20R = 1175
NOW it will work

Answer 12

are the Scotts using 35 or 37 L of water?

Answer 13

There is another way you can do this using:
S + R = 40 and
35S + 20R = 1175

Multiply the first equation by -20, which will give you
-20S + -20R = -800

then add the above equation to 35S + 20R = 1175,

-20S + -20R = -800
35S + 20R = 1175

When you add them together you get:

15S = 375 solve for S, you get S = 25

Answer 14

if S = 25 hours, then R = 15 hours, but they also ask how much water each family used, so you would have to multiply 25 x 35L to get the amount of water used by the Scotts and 15 x 20L to get the amount of water used by the Rogers