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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- AkashdeepDeb

7 identical pumps => 6 hours
4 identical pumps => ? hours
Statement: More pumps, less time. Inversely proportional.
Solution: No. of pumps in 1st case * time taken in 1st case = no. of pumps in second case * time taken in 2nd case.
Think of it like this: 42 identical pumps would be needed to do it in 1 hour.

- anonymous

I dont understand why it's 7*6 @AkashdeepDeb

- anonymous

how do i even know what 7*6 calculates

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## More answers

- AkashdeepDeb

If I travel at 60 km/hr in a car, I can cover a distance x in 1 hour.
If I travel at 120 km/hr can you guess how much time it'll take to cover the same distance?

- anonymous

not sure

- AkashdeepDeb

7*6 calculates the volume of the pool, per se.
Basically, it remains constant, because, obviously, the pool's volume won't change.

- anonymous

hmmmmm.... trying to process this in my head

- anonymous

60*x / 120

- AkashdeepDeb

Ohkay. Let me use a similar example.
I want to right a book with a fixed number of words.
I can right 30 words per minute for 10 minutes.
If I can increase my speed to 60 words per minute, how much time will it take me to write the book?
See, what's happening here. I STILL have to write the same number of words!
If I can finish writing a book by writing at 30 words per minute for 10 minutes, I am writing 30 * 10 words = 300 words.
Now, if I write a 60 words per minute, I still have to write 300 words. That would take me 300/60 = 5 minutes to write.

- anonymous

can i do proportions with this?

- AkashdeepDeb

It's just like the basic equation: \(Time * Speed = Distance\)
The Distance, always remains constant.
In your case, the volume of pool is constant.

- anonymous

ok got it i think

- dan815

did u want some help with this, you bumped it up?

- anonymous

do u have a different interpretation?

- dan815

well there was a great trick suggested already

- dan815

let h be hours
7*6 = 4*h,
is a nice simplification, but the logic behind it, u have to think about it a little

- anonymous

why is it 7*6

- dan815

it doesnt have to it, this relation just exists between the 7 and 4 and the number of hours

- dan815

Here is another way to approach the problem, okay lets just say there is some work W, that needs to be done

- anonymous

yes

- dan815

7 pumps take 6 hours to complete this work,, which means each pump worked for 6 hours

- dan815

7 of these pumps worked for 6 hours in total

- anonymous

yes

- dan815

okay so lets say it was just 1 pump, its pretty logical to say this 1 pump has to work 7 times more hours right

- anonymous

yea

- dan815

okay so

- dan815

now when its 4 pumps, that means we have to work 7/4 times more xD

- anonymous

yea

- dan815

so 7/4 * 6 is our hours,

- anonymous

hmmmm i see

- anonymous

so it's proportions?

- dan815

here is another way that 7*6 = 4*h relationship comes up

- dan815

i forgot what i was about to say xD

- Baseballguy101

i always solve problems like this another way. if you have 7 pumps that empty a pool in 6 hours you can divide the amount of pumps by the time. so 7/6 then times it by the amount of pumps you're using now. so I would use the equation (7/6)*4

- anonymous

lol

- Baseballguy101

does that make sense to you?

- anonymous

kinda...

- anonymous

okay i think i got it... thanks guys

- Baseballguy101

no problem there are many ways to solve a problem just use the easiest for you!

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