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?

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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?

Mathematics
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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.
I dont understand why it's 7*6 @AkashdeepDeb
how do i even know what 7*6 calculates

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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?
not sure
7*6 calculates the volume of the pool, per se. Basically, it remains constant, because, obviously, the pool's volume won't change.
hmmmmm.... trying to process this in my head
60*x / 120
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.
can i do proportions with this?
It's just like the basic equation: \(Time * Speed = Distance\) The Distance, always remains constant. In your case, the volume of pool is constant.
ok got it i think
did u want some help with this, you bumped it up?
do u have a different interpretation?
well there was a great trick suggested already
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
why is it 7*6
it doesnt have to it, this relation just exists between the 7 and 4 and the number of hours
Here is another way to approach the problem, okay lets just say there is some work W, that needs to be done
yes
7 pumps take 6 hours to complete this work,, which means each pump worked for 6 hours
7 of these pumps worked for 6 hours in total
yes
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
yea
okay so
now when its 4 pumps, that means we have to work 7/4 times more xD
yea
so 7/4 * 6 is our hours,
hmmmm i see
so it's proportions?
here is another way that 7*6 = 4*h relationship comes up
i forgot what i was about to say xD
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
lol
does that make sense to you?
kinda...
okay i think i got it... thanks guys
no problem there are many ways to solve a problem just use the easiest for you!

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