Combine two workers: A and B can complete a piece of work in 6 days and 12 days respectively. If both work together at their constant rates, in how many days will the job be finished?

Introduction / Context:
Classic combined-work calculation: sum individual daily rates to get the team rate, then invert to find the total time needed when both work simultaneously without interruptions or interference.

Given Data / Assumptions:

• A’s time = 6 days ⇒ rate = 1/6 job/day.
• B’s time = 12 days ⇒ rate = 1/12 job/day.
• Work is 1 job; rates add when working together.

Concept / Approach:
Team rate = 1/6 + 1/12 = 1/4 job/day. Total time = 1 ÷ team rate = 4 days.

Step-by-Step Solution:
1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4. Time = 1 / (1/4) = 4 days.

Verification / Alternative check:
As a reasonableness check, the combined time (4) is less than the smaller of 6 and 12, which is expected.

Why Other Options Are Wrong:
6 or 9 days exceed the correct joint time; 18 is far too large for a team that includes a faster worker.

Common Pitfalls:
Averaging 6 and 12 to get 9 instead of adding rates. Always add rates for combined work.

Final Answer:
4 days