Work completion after partial progress by a faster coworker A can finish a job in 10 days, while B can finish the same job in 6 days. B works alone for the first 4 days. How long will A take to complete the remaining work, starting from that point?

Introduction / Context:Questions involving “work done before/after” test your ability to compute partial work using individual rates and then convert the remaining work into time for another worker. This problem features two workers with different efficiencies and a hand-off in the middle.

Given Data / Assumptions:

• A completes the job in 10 days.
• B completes the job in 6 days.
• B works alone for the first 4 days.
• Total work is normalized to 1 unit.

Concept / Approach:The rate approach: If a worker completes a job in T days, the daily rate is 1/T. Work done = rate * time. Remaining work = total work − completed work.

Step-by-Step Solution:

Verification / Alternative check:Convert to hours if desired: 10/3 days ≈ 3.333... days. Multiplying A’s rate 1/10 by 10/3 yields exactly 1/3 of the job, matching the remaining portion.

Why Other Options Are Wrong:

• 11/3 days: Overestimates the needed time; A would do more than the remaining 1/3.
• 7/3 days: Underestimates; A would not finish the remaining part.
• 4 days: Assumes slower-than-necessary completion; A’s rate is sufficient to do it in less.
• None of these: Incorrect because 10/3 is available.

Common Pitfalls:Mixing up who worked first, or adding rates/time incorrectly. Always compute remaining work correctly before dividing by the finisher’s rate.

Final Answer:10/3 days