Question

Please help me solve the algebra word problem:

The Wilson family and the Alexander family each used their sprinklers last summer. The water output rate for the Wilson family’s sprinkler was 30L per hour. The water out put rate for the Alexander family’s sprinkler was 25L per hour. The families used their sprinklers for a combined total of 45 hour, resulting in a total output of 1200L. How long was each sprinkler used?

Wilson family sprinkler = _______ hours

Alexander family’s sprinkler = ______ hours

Answer 1

If you let w = the number of hours the Wilson sprinkler was used, then

45 - w = the number of hours the Alexander sprinkler was used.

30w + 25(45 - w) = 1200

So, now, just solve for "w". Are you able to do that?

Answer 2

No, I tried and my answers were wrong, I do not understand the substitution theory.

Answer 3

30w + 25(45 - w) = 1200 -> 30w - 25w = 1200 - (25)(45)

(30 - 25)w = 75 -> 5w = 75 -> w = 15

So, the Wilson's usage was 15 hours while the Alexander's usage was 30.

In that initial equation: 30w + 25(45 - w) = 1200

this is actually:

[30 (lit/hr)](w hr) + [25 (lit/hr)][(45 - w)hr] = 1200 lit -> "hrs" cancels

And the Alexander's usage is 45 - w because both usages have to add to 45

Answer 4

What you have is actually 2 equations in 2 unknowns:

30w + 25a = 1200 and w + a = 45

a = 45 - w (from the second equation) so you take that "45 - w" and put THAT in the first equation where you see the "a".

Answer 5

The example shows what your equation shows, and I understand what is written but not how you reached the answers.how did you get 75? Just viewed your last statement I understand what you have written but not how your received the answer.

Answer 6

I am asking exactly how to reach the solution, is it by dividing a then multiplying it by w?

Answer 7

The Wilson family used more water why is the number of hours less than the Alexander family?

Answer 8

The 75 came from:

1200 - (25)(45) -> 1200 - 1125 -> 75

Here, let me fill in a few more steps:

30w + 25(45 - w) = 1200

30w + (25)(45) - 25w = 1200

30w - 25w + (25)(45) = 1200

(30 - 25)w = 1200 - (25)(45)

5w = 1200 - 1125 = 75

5w = 75 -> w = 75 / 5 = 15

Answer 9

I understand that

Answer 10

So, you're all set?

Answer 11

Wouldn't the 15 belong to the Alexander family since we received that answer from using the 25 L?

Answer 12

No, because in my first post, we established that "w" (w for Wilson, but we could have used any variable) is the # of hours of Wilson's usage. So, when we solved for "w", that value pertains to the Wilsons.

Answer 13

At this point, you might want to step away from "how to solve it" and just plug the values back in to see how it does indeed work.

Answer 14

T.C. Thank you so very much. You deserve a medal, please tell me how to give you a medal, this is just my second time on this site.

Answer 15

oh, ok, you just hit "best response" (the blue box) by my name. And it was very nice working with you!

Answer 16

Good luck to you in all of your studies and thx for the recognition! @Tuiti You are very welcome for the help!

Answer 17

Just gave you a medal and it is so nice to have someone explain what seems to be Greek to me. Thank you again!

Answer 18

Before you go, this was a good problem for "2 equations in 2 variables". We went through it in fairly big detail, so you or anyone would benefit from just going over it at least one more time.

Answer 19

I hope to work with you again, thanks for being here for us!

Answer 20

You made my day! @Tuiti

Answer 21

LOL! You made mine too!

Answer 22

T.C can you help me to solve the compound inequality. Both signs are less than or equal to, it sometimes does not show up when I copy and paste.

4y- 2 ≤ 22 or 3y-5 ≤ 1

Thanks Tuiti

Answer 23

T.C can you help me to solve the compound inequality. Both signs are less than or equal to, it sometimes does not show up when I copy and paste.

4y- 2 ≤ 22 or 3y-5 ≤ 1

The answer has to be in interval notation.