Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?

- anonymous

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- anonymous

@satellite73 can we take this one slow too?

- anonymous

sure unit rate again

- anonymous

So 7/6 will be how much 1 pump can empty a pool

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## More answers

- anonymous

careful

- anonymous

lets start with how much 7 pumps do per hour

- anonymous

isn't that what 7/6 finds?

- anonymous

7 pumps take 6 hours, so 7 pumps do \(\frac{1}{6}\) per hour

- anonymous

oh okay

- anonymous

how much does one pump do? don't multiply by 7, divide (like last time)

- anonymous

1/42

- anonymous

ok good
now each pump does \(\frac{1}{42}\) per hour, how much does 4 pumps do (this time multiply)

- anonymous

4/42

- anonymous

right

- anonymous

or you can reduce to get \(\frac{2}{21}\)

- anonymous

hmmmm did we do something wrong? my answer say 42/4 = 10 1/2

- anonymous

you want to see how long it takes to do one job,

- anonymous

solve
\[\frac{2}{21}T=1\] making
\[T=\frac{21}{2}\]

- anonymous

no we didn't do anything wrong, we just were not done yet
we got the unit rate at \(\frac{2}{21}\) but we need the total time

- anonymous

ohhh okay

- anonymous

they do 2/21 of a job per hour, takes 21/2 hours to do one job

- anonymous

ohhh okay

- anonymous

there may have been a quicker way to do this, but it is good to know how to get the unit rate so you can do all kinds of problems with it

- anonymous

hmmm ok

- anonymous

so do we now multiply by 4?

- anonymous

no now we are done

- anonymous

ohhh okay this is a different method i got it now

- anonymous

we got the unit rate of \(\frac{1}{42}\) that was pump per hour

- anonymous

then we multiplied by 4 to get the rate for 4 pumps and got \(\frac{2}{21}\)

- anonymous

ahhhh ic

- anonymous

then we solved
\[\frac{2}{21}T=1\] the 1 being one pool

- anonymous

if it was two pools it would have been
\[\frac{2}{21}=2\]

- anonymous

hmmm okay i think i understand now i'll review the last 2 problems we did a couple of times

- anonymous

ok if you get stuck let me know

- anonymous

i will thanks <333

- anonymous

we can make one up and do it now if you like

- anonymous

yes yes that would help even more

- anonymous

see that they are not that hard and are largely the same

- anonymous

yea

- anonymous

you want me to make it up, or you want to?

- anonymous

can u ?

- anonymous

k
they numbers might not come out real nice if i make it up off the top of my head, but no matter

- anonymous

ok

- anonymous

it takes 5 hours for 8 men to build one wall
how long would it take 10 men to build 2 walls (sexist i now but whatever)

- anonymous

first find the unit rate for one man
let me know when you think you have it

- anonymous

1/8 divided by 5 = 1/40

- anonymous

yay!

- anonymous

now the rate for 10 men

- anonymous

1/40 * 10 = 10/40 = 1/4

- anonymous

ok good
now how long to build 2 walls

- anonymous

1/4 * 2= 2/4= 1/2

- anonymous

aw damn we were doing so well

- anonymous

oh crap...

- anonymous

not going to take half an hour !

- anonymous

now we need to go slow
either we solve
\[\frac{1}{4}T=2\]

- anonymous

ohhhhhh yeaaaa thats right so 8

- anonymous

yup

- anonymous

ok i'll keep practicing this

- anonymous

almost got it 100% thanks satellite

- anonymous

ok, i think it is getting easier though right? first part went quick

- anonymous

yw

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