Question

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?

Answer 1

@satellite73 can we take this one slow too?

Answer 2

sure unit rate again

Answer 3

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

Answer 4

careful

Answer 5

lets start with how much 7 pumps do per hour

Answer 6

isn't that what 7/6 finds?

Answer 7

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

Answer 8

oh okay

Answer 9

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

Answer 10

1/42

Answer 11

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

Answer 12

4/42

Answer 13

right

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

ohhh okay

Answer 20

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

Answer 21

ohhh okay

Answer 22

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

Answer 23

hmmm ok

Answer 24

so do we now multiply by 4?

Answer 25

no now we are done

Answer 26

ohhh okay this is a different method i got it now

Answer 27

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

Answer 28

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

Answer 29

ahhhh ic

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

ok if you get stuck let me know

Answer 34

i will thanks <333

Answer 35

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

Answer 36

yes yes that would help even more

Answer 37

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

Answer 38

yea

Answer 39

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

Answer 40

can u ?

Answer 41

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

Answer 42

ok

Answer 43

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)

Answer 44

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

Answer 45

1/8 divided by 5 = 1/40

Answer 46

yay!

Answer 47

now the rate for 10 men

Answer 48

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

Answer 49

ok good
now how long to build 2 walls

Answer 50

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

Answer 51

aw damn we were doing so well

Answer 52

oh crap...

Answer 53

not going to take half an hour !

Answer 54

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

Answer 55

ohhhhhh yeaaaa thats right so 8

Answer 56

yup

Answer 57

ok i'll keep practicing this

Answer 58

almost got it 100% thanks satellite

Answer 59

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

Answer 60

yw