Combined daily work fraction: A can complete a piece of work in 18 days and B can complete the same work in half of A’s time (i.e., 9 days). Working together, what fraction of the work do they complete in one day?

Introduction / Context: When two workers collaborate, their daily work fractions add. Given individual completion times, we can compute each daily rate and sum them to obtain the combined one-day fraction of the job completed.

Given Data / Assumptions:

• A’s time = 18 days ⇒ A’s rate = 1/18 job/day.
• B’s time = 9 days ⇒ B’s rate = 1/9 job/day.
• Total work = 1 job; rates are constant.

Concept / Approach: Combined rate = (1/18 + 1/9). This directly gives the fraction of the work done in a single day when they work together.

Step-by-Step Solution: 1/18 + 1/9 = 1/18 + 2/18 = 3/18 = 1/6. So, in one day together they complete 1/6 of the job.

Verification / Alternative check: Time together would be 1 ÷ (1/6) = 6 days, which lies between 9 and 18 days, as expected for combined work.

Why Other Options Are Wrong: 1/9 is A’s rate alone if B were slower (not the case). 2/5 and 2/7 are unrelated to these exact reciprocals.

Common Pitfalls: Averaging times instead of adding rates. Always combine work problems via rates, not raw days.

Final Answer: 1/6