There are two taps. Tap A takes 7 minutes to fill up a bucket and tap B takes 3 minutes to fill up the same bucket. Calculate the time it takes both Tap A and Tap B to fill up the same bucket ?

Question

That's all we were given. The answer must be in Seconds

Answer 1

Let's say the bucket has a capacity of 21L. In one minute tap A delivers 3L while tap B delivers 7L, so tap A will take 7 minutes to fill the bucket and tap B will take only 3 minutes. Together in one minute they can deliver 10L. It takes 2 minutes to deliver 20L. So to deliver 1L it will take 2/20=1/10 of a minute, that is, 6 seconds. So to deliver 21L it takes 2mins and 6secs (126 seconds).

Now, let's solve this using algebra. Let C=capacity of the bucket, then in one minute tap A delivers C/7 units while tap B delivers C/3 units. In one minute they deliver C/7+C/3 units. So it will take C/(C/7+C/3) minutes to deliver C units: the C's cancel out: 1/(1/7+1/3)=1/(10/21)=21/10=2.1 minutes.

This can be presented as the "harmonic" equation: 1/t=1/7+1/3 where t is the time when both taps fill the bucket.