Billy-joe and bob purchased a pool with a capacity of 60 gallons for his farm. one day, at 1 p. m., billy-joe placed a hose into the pool, filling it with water at a rate of 3 gal per hour. after 10 hours, horses and cows started drinking the water at a combined rate of 1 gal/hr. five hours later, bob noticed the animals drinking and placed a second hose in the pool which filled it at a rate of 2 gal/hr. at what time could bob declare the pool was full of water?

So you just want to separate these into parts first.

Part 1: The hose filling up the pool without any animals or other hoses.

Part 2: The hose filling up the pool with the horses and cows drinking.

Part 3: The hose filling up the pool with the horses and cows drinking and the second hose.

So just figure out how much got filled in each of the parts.

Part 1: lasted for 10 hours

Since it lasted for 10 hours, and there was a hose filling it with water at a rate of 3 gal per hour, we can multiply everything by 10/10. This sorta makes no sense, but basically what it is is:

* 10/10

Which then equals 30 gal / 10 hours

So now we know that Part 1 filled the pool with 30 gallons.

Part 2: So since there's a hose filling the pool and animals draining the pool, we want to find the rate that the pool is being filled here.

So since the animals are taking away 1 gal per every 3 gal the hose fills in, just subtract 1 from 3, to get 2 gal / h.

Do the same thing, except with 5/5, to get 10 gal/ 5 hours.

So Part 2: 10 gal.

So so far the pool has been filled with, 30 gallons, and 10 gallons. Therefore all together it's been filled with 40 gallons of water. Since the pool can hold 60 gallons, just subtract 40 gallons from 60 gallons to find the amount of space left needed to be filled.

60 - 40 = 20

So in Part 3, the two hoses and also the animals drinking had to result in 20 gallons of water being filled.

Since the first hose and the animals drinking made it so the rate that the pool was being filled 2 gal/h, you can just add 2 gal/h to that because of the second hose having a fill rate of 2 gal/h.

2 + 2 = 4

So the rate here was 4 gal / h

So basically, to get 20 gallons, you just want to multiply by 5/5. This results in 20 gal / 5 hours.

So Part 3: 5 hours.

If we go through all the parts,

Part 1: 10 hours
Part 2: 5 hours
Part 3: 5 hours

In total: 20 hours

Since you're looking for the time, just add 20 hours to the time. 

1 PM + 11 hours = 12 AM

9 hours remaining

12 AM + 9 hours = 9 AM

So at 9 AM Bob could declare the pool as full of water.