Three water pipes are used to fill a swimming pool. the 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. if all 3 pipes are opened at the same time, how long will it take all 3 together to fill the pool?

For 4 h. The first pipe fills the whole pool for 8 hours so from here we see that it fills 1/8 each hour. The second pipe fills it for 12 hours so it fills 1/12 each hour. The third pipe fills it for 24 hours so it fills 1/24 each hour. Now the three of them together fill 1/8 + 1/12 + 1/24 of the pool each hour. That equals: 1st pipe 3/24 of the pool each hour, the 2nd pipe 2/24 of the pool each hour and the 3rd 1/24 each hour. So, the three pipes together fill 3/24 + 2/24 + 1/24 each hour. That's 6/24 of the pool each hour.
1st hour: 6/24
2nd hour: 12/24
3rd hour: 18/24
4th hour: 24/24