One pipe fills a storage pool in 20 hours. A second pipe fills the same pool in 15 hours. when a third pipe is added and all three are used to fill the pool , it takes only 6 hours. Find how long it takes the third pipe todo the job.
One pipe fills a storage pool in 12 hours. A second pipe fills the same pool in 6 hours. When a third pipe is added and all three are used to fill the pool, it takes only 3 hours. Find how long it takes the third pipe to do the job.
Answer This
To solve this problem, we need to determine the rates at which each pipe fills the pool.
Let's assume that the first pipe can fill 1 pool per x hours. Therefore, its filling rate is 1/x.
Similarly, let's assume that the second pipe can fill 1 pool per y hours. Therefore, its filling rate is 1/y.
Given that the first pipe fills the pool in 20 hours, its rate is 1/20. And the second pipe fills the same pool in 15 hours, so its rate is 1/15.
When the third pipe is added, and all three pipes are used to fill the pool, it takes only 6 hours. Let's assume that the third pipe takes z hours to fill the pool, so its filling rate is 1/z.
Now, we can set up an equation to represent the combined rate at which all three pipes fill the pool:
1/20 + 1/15 + 1/z = 1/6
To solve for z and find how long it takes the third pipe to do the job, we need to rearrange the equation:
1/z = 1/6 - (1/20 + 1/15)
1/z = (5/30) - (3/60 + 2/60)
1/z = 5/30 - 5/60
1/z = (5 - 1)/60
1/z = 4/60
1/z = 1/15
Therefore, the third pipe takes 15 hours to fill the pool on its own.
If the 3rd pipe takes x hours,
1/6 = 1/20 + 1/15 + 1/x
x = 20