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?
Correct Answer: 10/3 days
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:
Rate of A = 1/10 per dayRate of B = 1/6 per dayWork done by B in 4 days = 4 * (1/6) = 2/3Remaining work after B = 1 − 2/3 = 1/3Time for A to do the remaining work = (1/3) / (1/10) = 10/3 daysVerification / 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