plzz help me i'm stuck on a word problem(time-work problem)?

Question

two taps A and B can fill a water tank in 9 minutes and 12 minutes. In what time the tank will be full, if B starts working 2 minutes after A starts working?

Answer 1

A fills 1/9 per minutes while B fills 1/12 per minute

A starts - after 2 minutes there is 7/9 empty
after, the fill at 1/9 + 1/12 = 4/36 + 3/36 = 7/36 per minute

Thus it takes 7/9 divided by 7/36 = 7/9 * 36/7 = 36/9 = 4 minutes

so 6 minutes in all.