Question

The Alexander family and the Torres family each used their sprinklers last summer. The water output rate for the Alexander family's sprinkler was 40L per hour. The water output rate for the Torres family's sprinkler was 30L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total water output of 2050L . How long was each sprinkler used?

Answer 1

Please help!

Answer 2

Well, set up some basic equations based on what you know. If 'a' is the Alexanders and 't' are the Torres's's's's's's. Then:
\[a + t = 60\]
\[40a + 30t = 2050\]

Answer 3

Then what would you do from there?

Answer 4

Well, solve for one variable in the easiest equation to solve. The first one looks really easy to me.

Answer 5

Would a=51.25 ?

Answer 6

No, it would not. Try to follow the logic here. Solve the first equation for one variable, either a or t.

Answer 7

Yeah wouldn't I make it so it was 40a=2050 by setting t to 0?

Answer 8

You're trying to go several steps ahead. Solve the first equation for either a or t.

Answer 9

Could you help me through steps or just explain to me what you got for the first equation because I'm lost.

Answer 10

Well we know that the total number of hours that each family used is 60. So the alexanders + the torreses = 60 (a + t = 60)

Answer 11

Yeah I understand that information

Answer 12

We also know that however much the alexanders used is 40 times that time, and however much the torreses used is 30 times that time. The total amount used was 2050. (40a + 30t = 2050)

Answer 13

So solve the first equation for either a or t. Thats the first step there. You COULD solve the second equation but it might make things a little more tedious.

Answer 14

So the first equation meaning a+t=60 ?

Answer 15

Yes.

Answer 16

a=60-t & t=60-a

Answer 17

That works, so now you know what 't' is. Plug 60-a in for 't' in the second equation. Distribute and solve for a.

Answer 18

So set it up as: a+60-a=60

Answer 19

I doubt that's right..

Answer 20

No, look at the SECOND equation now. Since t = 60-a, instead of 't', use 60-a.
\[40a + 30(60 - a) = 2050\]

Answer 21

Now you have only a's, and no t's.

Answer 22

a=25

Answer 23

Thats correct, now plug 'a' BACK into the ORIGINAL equation (a + t = 60) to get t.

Answer 24

t=35

Answer 25

Thats it. You can verify by plugging both t and a back into both equations to see if they both hold up. (They do, already checked) ;)

Answer 26

Thanks soo much!

Answer 27

No prob