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The family and the family each used their sprinklers last…

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The Cooper family and...

The Cooper family and the Smith family each used their sprinklers last summer. The water output rate for the Cooper family's sprinkler was 15 L per hour. The water output rate for the Smith family's sprinkler was 30 L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 975 L. How long was each sprinkler used? im having problems answering that question

Submitted: 3 months ago.Category: Pre-Calculus
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1/9/2018
Tutor: Ryan, Engineer replied 3 months ago
Ryan
Ryan, Engineer
Category: Pre-Calculus
Satisfied Customers: 9,171
Experience: B.S. in Civil Engineering
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Hi,Thank you for using the site. I will be happy to help you with this problem. I’ll have the solution posted for you just as soon as I finish typing it up.Thanks,Ryan
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Tutor: Ryan, Engineer replied 3 months ago

Hi again,

Please see the document at the following link for the solution to this problem:

Sprinklers

Please let me know if you have any trouble accessing the file at that link, and please feel free to ask if you have any questions about this solution.

Thanks,

Ryan

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Customer reply replied 3 months ago
It says the url is blocked
Tutor: Ryan, Engineer replied 3 months ago

Oh, ok, hang on just a second and I'll post the solution in a different manner.

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Tutor: Ryan, Engineer replied 3 months ago

Please let me know if this link works for you.

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Customer reply replied 3 months ago
Is it possible for me to ask another question or will I get charged?
Tutor: Ryan, Engineer replied 3 months ago

Yes, that's fine.

(Please note, however, that it would be better to post all of your questions to begin with, so that the expert who replies to you can make an informed decision about whether to take on the work.)

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Customer reply replied 3 months ago
I apologize, I didn't know I was supposed to do that. here is my question,Felipe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 6 clients who did Plan A, and 5 who did Plan B. On Thursday there were 2 clients who did Plan A, and 3 who did Plan B. Felipe trained his Wednesday clients for a total of 7 hours and his Thursday clients for a total of 3 hours. How long does each of the workout plans last?
Tutor: Ryan, Engineer replied 3 months ago

It's ok. I understand that this is your first time using the site, and that it can be confusing. No worries.

I'll get this back to you as quickly as I can type it up.

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Customer reply replied 3 months ago
ok
Tutor: Ryan, Engineer replied 3 months ago

For this one, let A represent the number of hours required for Plan A, and let B represent the number of hours required for Plan B.

For Wednesday, then, the total time would be 6A + 5B, which is equal to 7 hours.

Similarly, on Thursday, the total time would be 2A + 3B, which is equal to 3 hours.

This gives a system of two equations:

6A + 5B = 7

2A + 3B = 3

Multiplying the second equation through by 3 then gives a new system:

6A + 5B = 7

6A + 9B = 9

Subtracting the first equation from the second equation leaves:

4B = 2

B = 2/4 = 1/2 hour (or 30 minutes)

Substituting this into the equation 2A + 3B = 3 (this equation is chosen simply because the coefficients are smaller, which makes the calculation easier) gives:

2A + 3(1/2) = 3

2A + 3/2 = 3

2A = 3 - 3/2

2A = 3/2

A = 3/4 hour (or 45 minutes)

Solution: Plan A takes 45 minutes and Plan B takes 30 minutes.

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