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?
rates of each of the pipes are 1/8 pools per hour, 1/12 pools per hour, and 24 pools per hour.
the combined rate would be
(1/8 + 1/12 + 1/24) pools per hour
= 1/4 units per hour
Time using combined rate = 1 pool/(1 pool/4) hours
= 4 hours
(the "pool" unit canceled)
What they said :)
Well, when it comes to filling swimming pools, it's always better to have friends to help you out. So, let's see how our three water pipes get along!
The 1st pipe takes 8 hours to fill the pool, which means it can fill 1/8th of the pool per hour. The 2nd pipe takes 12 hours, so it can fill 1/12th of the pool per hour. Finally, the 3rd pipe takes 24 hours, meaning it can fill 1/24th of the pool per hour.
To determine how long it will take all three pipes working together, we need to add up their individual rates. So, 1/8 + 1/12 + 1/24 = 6/48 + 4/48 + 2/48 = 12/48 = 1/4.
Hence, all three pipes together can fill 1/4th of the pool per hour. To fill the whole pool, it will take four times as long, which is 4 hours.
So, with the help of all three pipes, they will fill the pool in 4 hours, making it a solid team effort!
To find out how long it will take for all three pipes to fill the pool together, we can use the concept of rates.
The first pipe fills the pool in 8 hours, which means it has a rate of 1 pool per 8 hours, or 1/8 pool per hour.
The second pipe fills the pool in 12 hours, so its rate is 1/12 pool per hour.
The third pipe fills the pool in 24 hours, which gives a rate of 1/24 pool per hour.
To calculate the combined rate when all three pipes are opened simultaneously, we simply add up their individual rates:
1/8 + 1/12 + 1/24 = (3/24) + (2/24) + (1/24) = 6/24 = 1/4
The combined rate is 1/4 pool per hour.
Therefore, it will take all three pipes working together 4 hours to fill the pool.