Question

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

@Hero Help preaze e.e

Answer 2

@Shadow

Answer 3

@dude

Answer 4

Well, I really just use an equation to solve this one

Answer 5

Let \(A\) represent the time it takes person \(A\) to do the job alone and \(B\) represent the time it takes person \(B\) to do the job alone. Then \(t\) represents the time it takes both \(A\) and \(B\) to do the job together as represented by:
\(t = \dfrac{AB}{A + B}\)

Answer 6

So this this case, we can actually use \(J\) and \(M\) for variables

Answer 7

\(t = \dfrac{JM}{J + M}\)

where \(J\) represents how fast Jean can fill the pool and \(M\) represents how fast Mark an fill the pool.

Answer 8

okie so it would look like.....

\[t=\frac{ (8)(12) }{ 8+12 }\]

Answer 9

like dis???

Answer 10

Very nice :)

Answer 11

Yes correct. Now try to solve for \(t\) in fraction form. Don't reduce to decimals.

Answer 12

Try to write it as a mixed fraction.

Answer 13

okie let me see here

Answer 14

the only thing i can think of is \[4\frac{ 16 }{ 20}\] ?????? this is a guess and the only thing i can think of

Answer 15

Reduce the fraction

Answer 16

It's better to write it as \(4 + \dfrac{16}{20}\)

Answer 17

Writing it the other way implies multiplying 4 times 16

Answer 18

ok so \[4+\frac{ 16 }{ 20 }\]
\[\frac{ 16 }{ 20 }= \frac{ 4 }{ 5 }\]
so it would be \[4+\frac{ 4 }{ 5 }\]
convert it to fraction
\[\frac{ 4*5 }{ 5}+\frac{ 4 }{ 5 }\]

Answer 19

am i correct so far?

Answer 20

\(4 + \dfrac{4}{5}\) is good enough

Answer 21

oh okie e.e

Answer 22

Now you have to convert the 4/5 to minutes using a proportion

Answer 23

You have 4 hours and then 4/5 of an hour but the 4/5ths is meaningless because it doesn't represent a full hour so you have to convert it to minutes using the following proportion:

\(\dfrac{4}{5} = \dfrac{x}{60}\)

Answer 24

so it would take a third of the time if they did it together

Answer 25

\(4 + \dfrac{4}{5}\) means it will take four hours plus a fraction of an hour. We have to interpret what that fraction of an hour is in minutes. So solve the proportion above.

Answer 26

OOHHH i think i got it

\[\frac{ 4 }{ 5 }=\frac{ 48 }{ 60}\]

i could be wrong but i think this is the answer im looking for

Answer 27

Looks right to me. So basically it takes 4 hours and 48 minutes for them to do the same job working together. These problems are a lesson in the power of working together to accomplish tasks. You could do it alone but it would take much longer. If I had to do a job and I was told I had 12 hours to do it but my good ole buddy pal is with me and we could easily do it faster if we worked together, I'd rather take the fastest route and save 7 hours.

Answer 28

so all together it would look like

\[t=\frac{ JM }{ J+M }\]
\[t=\frac{ (8) (12)}{ 8+12 }\]
Write in a mixed fraction
\[4+\frac{ 16 }{ 20 }\]
\[reduce \frac{ 16 }{ 20 }=\frac{ 4 }{ 5 }\]
\[4+\frac{ 4 }{ 5 }\]
\[\frac{ 4 }{ 5}=\frac{ x }{ 60 }\]
\[x=48\]
\[\frac{ 4 }{ 5}=\frac{ 48 }{ 60 }\]
Meaning the time it takes to fill the pool working together would take 4 hours and 48 minutes

Answer 29

Well, you'd still have to put explanations in full sentences at each step.

Answer 30

Which should not be difficult for you

Answer 31

right but over all this is the answer and how it should look

Answer 32

Yes

Answer 33

thank you!
Is there anyway you could help with one more thats like this one

Answer 34

Only thing is, your teacher might ask you where you got the equation. Just say you got it from Hero

Answer 35

x'D you got it

Answer 36

She might ask how did you derive it though. Which would be even worse

Answer 37

i dont think so my teacher just see's the right answer and there like "pass" he doesnt ask much questions like that

Answer 38

Great job on this btw. I can tell you're eager to learn and teachable