A can complete a work in 20 days, while B can complete the same work in 30 days. If both A and B work together, in how many days will they complete the entire work?

Question: A can complete a work in 20 days, while B can complete the same work in 30 days. If both A and B work together, in how many days will they complete the entire work?

Solution:
A's 1 day work = 1/20
B's 1 day work = 1/30
Together 1 day work = 1/20 + 1/30
= (3 + 2)/60 = 5/60 = 1/12

∴ Total time = 1/Combined work rate
= 1/(1/12) days
= 12 days