:lol:

OK, here it is:

My swimming pool has 4 fill pipes, and all are different sizes. If you only use one at a time, the first can fill the entire pool with water in two days, the second in three days, the third in four days, and the last one can fill the pool in 6 hours.

How long will it take to fill the pool using all 4 pipes together? And no, there is no flow reduction because they are all open. I've got an unlimited supply at constant pressure!

Answer: The rate of the first faucet can be read as 1 "pool per 2 days", the second faucet 1 "pool per 3 days", and so on. Because the amount of time following the "per" in each rate is different, we can't compare them the way we need to. So, we'll standardize our units. Let's convert each rate to a unit representing "amount of pool filled per hour" (which we'll denote by p/h). Since each faucet takes more than an hour to fill the entire pool, each rate is going to be a fractional value.

The first faucet takes 2 days to fill the pool. There are 48 hours in 2 days, so this faucet has a rate of 1/48 p/h. Similarly, the rates of the second, third, and fourth faucets respectively are 1/72, 1/96, and 1/6. With these standardized units, we now turn to our formula.

Since we are using all four faucets at once, their combined rate of speed is simply the sum of their individual speeds. This gives us a combined rate of

1/48 + 1/72 + 1/96 + 1/6 = 61/288 p/h

Since the value for "d" in our formula represents the amount of pools filled, and we are only going to fill one pool, we will give it a value of 1. So, our formula gives us

1 = (61/288)t

t = 1/(61/288)

t = 288/61 ~ 4.7213 ~ 4 hours 43 minutes 17 seconds

Here is how I decided to award points. Go Steelers was the first answerer with 4:14:16.72. I would normally award lots of points, but I hate the steelers. Silvergoat came in at 4.7 hours, which I assume is correct. Since neither showed their work, I have to assume they both cheated and I am awarding the points to The Black Phantom, who won because he didn't attempt an answer.