Time and Work — Individual vs. Combined Rates A can complete the work alone in 6 days, and B can complete the same work alone in 3 days. If A and B work together from start to finish, in how many days will they complete the entire work?

Introduction / Context:This time-and-work question tests your ability to convert individual completion times into rates, add those rates for combined work, and then invert the sum to find the total time. It is a foundational technique used in aptitude tests and project-planning scenarios.

Given Data / Assumptions:

• A alone finishes in 6 days.
• B alone finishes in 3 days.
• They both work together continuously at constant rates.

Concept / Approach:Define one full job as 1 unit of work. The work rate of a person is 1/(their time). Combined work rate is the sum of individual rates. Time to finish = 1/(combined rate).

Step-by-Step Solution:A's rate = 1/6 job per day.B's rate = 1/3 job per day.Combined rate = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 job per day.Total time = 1 / (1/2) = 2 days.

Verification / Alternative check:If they complete half the job per day, then after 2 days the entire job is done. This matches the computed time exactly.

Why Other Options Are Wrong:3, 4, and 5 days imply slower combined rates than actually achieved. 6 days equals A's solo time and ignores B's contribution.

Common Pitfalls:Adding times directly (e.g., 6 + 3) or averaging 6 and 3 is incorrect. You must add rates (reciprocals of times), not the times themselves.

Final Answer:2 days