It takes three identical water pumps 8 hours to fill a pool. How long would it take four of the same pumps to fill the pool?

Accepted Solution

Itll take four pumps 6 hours to fill the pool with water. And heres how we get to that conclusion: Logically, the thing that would make calculating how much time would it take for four (or any other number) pumps to fill the pool much, much simpler, would be knowing how much water goes through one pump in one hour. And luckily, this can be calculated from the data given above. Basically, if three pumps fill the pool in 8 hours, this means one pump fills 1/3 of the pool in this time. Now, since the exact amount of water goes through the pump at any point, this means that in order to fill 1/3 of the pool with one pump, thered be 1/8 of the total amount of water that goes through it (in this case, 1/3 of the pool) every hour. Or, one pump would fill 1/8 * 1/3 in one hour. This is 1/24. And its just smooth sailing from here on. If one pump fills 1/24 of the pool in an hour, four pumps fill 4*1/24, or 1/6 in the same time. So if the four pumps fill out 1/6 of the pool in one hour, theyd need to do this 6 times to fill the whole pool. Or, rather, 6 hours.