Question

Need help, please.

Jean and Mark are going to fill a pool with 2 different sized hoses. Jean can fill the pool in 8 hours, while Mark can complete it in 12 hours. Their supervisor thinks that the job will take 10 hours to complete if they work together. Explain each step in solving this equation and determine if the supervisor is correct or not.

Answer 1

Jean fills 1/8 of the pool per hour. Do you understand that?

Answer 2

Yes, and then mark it would be 1/12?

Answer 3

Yes.

Answer 4

So what part of the pool could Jean fill in 3 hours?

Answer 5

1/3 ?

Answer 6

no.

Answer 7

This is such a key concept. Let's see if you can understand it in a different way. Have you ever had a job of any kind? Maybe babysitting or something?

Answer 8

I've watched my brothers dog a few times

Answer 9

How much did you make each day for watching the dog?

Answer 10

Well, he's still a puppy so I had to watch him usualy from 8 in the morning until 9 when my mom got home

Answer 11

Did you get paid?

Answer 12

Usually he would buy me a new game or donuts or something lol

Answer 13

Well, let's just say you had a babysitting job and you made $5 per hour. Then you would make $5 times 3 in 3 hours. Do you understand that?

Answer 14

Yes, because if it's 5 dollars an hour and I worked for 3, i would do the 5 x 3 to find out how much I would make?

Answer 15

Yes. Very good.

Answer 16

Now if you baby sat for h hours you would make $5 times h or 5h dollars. Do you understand that?

Answer 17

Yes, because in this situation you don't know how many hours I've worked

Answer 18

Now let's go back to the pool.

Answer 19

Jean fills 1/8 pool each hour. So in x hours she would fill 1/8 times x or (1/8)(x) or
\[\frac{x}{8}\] pools

Answer 20

And if you understand that, then tell me how many pools Mark fills in x hours

Answer 21

If mark fills 1/12 of pool each hour. Then mark would in x hours fill 1/12 times x or (1/12)(x)
and it would be
\[\frac{ x }{ 12} ?\]

Answer 22

Perfect

Answer 23

Now together they fill 1 pool so add what Jean does to what Mark does and set it equal to 1

Answer 24

so \[\frac{ x }{ 8} + \frac{ x }{ 12 }\] thats how to set it up right?

Answer 25

Yes and put = 1

Answer 26

alright so, would I need to find a common denominator?

Answer 27

Yes. Which is 24. So multiply both sides of the equation by 24

Answer 28

\[\frac{ x }{ 8 } (24) + \frac{ x }{ 12 } (24) = 1\]
so now it's \[\frac{ 24x }{ 24 } + \frac{ 24x}{ 24}\] sorry if I get this totally incorrect

Answer 29

\[\frac{x}{8}\times \frac{24}{1}= 3x\]
because the 8 cancels into the 24