With the tap A is running alone the bucket is filled in 12 minutes and when tap B alone is running the bucket is filled in 18 minutes.
The rate at which tap A can fill the bucket is 1/12 per minute. The rate at which tap B can fill the bucket is 1/18 per minute.
When both the taps are running the bucket is filled at the rate 1/12 + 1/18 = 5/36
To fill the bucket it takes 36/5 = 7.2 minutes
The bucket is filled in 7.2 minutes when both the taps are running.
We can also set up an equation to solve this work problem.
We are given that tap A can fill a bucket by itself in 12 minutes and tap B can fill the bucket in 18 minutes. We are asked how long it will take for the two taps running together to fill the bucket.
=> let x = total job time for both working together
=> let 1/12x = time it takes for tap A to fill the bucket
=> let 1/18x = time it takes for tap B to fill the bucket
=> The entire completion of the job will be equal to 1
=> 1/12 x + 1/18x = 1 (completed job)
=> 36 [1/12 x + 1/18x = 1] (to clear fractions)
=> 3x + 2x = 36
=> 5x = 36
=> x =36/5 or 7.2 minutes
Both taps running together will fill the bucket in 7.2 minutes.