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

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.

Answer 2

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

Answer 3

how do i even know what 7*6 calculates

Answer 4

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?

Answer 5

not sure

Answer 6

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

Answer 7

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

Answer 8

60*x / 120

Answer 9

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.

Answer 10

can i do proportions with this?

Answer 11

It's just like the basic equation: \(Time * Speed = Distance\)
The Distance, always remains constant.

In your case, the volume of pool is constant.

Answer 12

ok got it i think

Answer 13

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

Answer 14

do u have a different interpretation?

Answer 15

well there was a great trick suggested already

Answer 16

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

Answer 17

why is it 7*6

Answer 18

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

Answer 19

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

Answer 20

yes

Answer 21

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

Answer 22

7 of these pumps worked for 6 hours in total

Answer 23

yes

Answer 24

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

Answer 25

yea

Answer 26

okay so

Answer 27

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

Answer 28

yea

Answer 29

so 7/4 * 6 is our hours,

Answer 30

hmmmm i see

Answer 31

so it's proportions?

Answer 32

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

Answer 33

i forgot what i was about to say xD

Answer 34

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

Answer 35

lol

Answer 36

does that make sense to you?

Answer 37

kinda...

Answer 38

okay i think i got it... thanks guys

Answer 39

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