When three pipes fill a pool, they can finish in 12 hours. Two of the pipes can finish in 18 hours if they are working together. How long would it take a third pipe to fill the pool on its own?
consider the two pipes to be a single pipe that fills it in 18 hrs. So, now we have
1/18 + 1/x = 1/12
To find the time it would take for the third pipe to fill the pool on its own, we can approach this problem using the concept of "work rates."
Let's assume that the work rate (amount of work done per unit of time) of the third pipe is represented by "A" (in pools/hour). The combined work rate of the first two pipes working together is represented by "B" (in pools/hour). We want to find the work rate of the third pipe on its own.
From the given information, we know that:
1. The three pipes can fill the pool in 12 hours, so their combined work rate is 1 pool per 12 hours, or 1/12 pools per hour: 1/12 = A + B + B.
2. The first two pipes can fill the pool in 18 hours when working together, so their combined work rate is 1 pool per 18 hours, or 1/18 pools per hour: 1/18 = B + B.
Let's solve for B in the second equation:
1/18 - B = B
1/18 = 2B
B = 1/36 pools per hour
Now we can substitute the value of B into the first equation:
1/12 = A + 1/36 + 1/36
1/12 = A + 2/36
1/12 = A + 1/18
1/12 - 1/18 = A
3/36 - 2/36 = A
1/36 = A
The work rate of the third pipe, represented by A, is 1/36 pools per hour. This means that the third pipe can fill the pool on its own in 36 hours.
Therefore, it would take the third pipe 36 hours to fill the pool on its own.