# 2 taps A and B can fill a bucket in 12 and 18 minutes resp. How long will it take both the taps to fill the bucket.

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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.**

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.**