Three typists A, B, and C work on the same report. A alone can finish the report in 16 hours; B alone in 20 hours; C alone in 24 hours. All three start typing together at 9:00 a.m. At exactly 1:00 p.m. (after 4 hours), typist A stops and leaves the task. B and C continue and finish the remaining work together. Approximately at what time (clock time) is the report fully typed?

Introduction / Context:Time-and-work problems often require converting individual times to rates, adding rates for simultaneous work, and then tracking partial progress across phases. Here, three typists start together; one leaves after 4 hours, and the others finish. We must compute the exact finish time from the start at 9:00 a.m.

Given Data / Assumptions:

• A's time = 16 h ⇒ rate = 1/16 report per hour.
• B's time = 20 h ⇒ rate = 1/20 per hour.
• C's time = 24 h ⇒ rate = 1/24 per hour.
• All start at 9:00 a.m.; A stops at 1:00 p.m. (4 hours).

Concept / Approach:Use unit-work method. Total work W = 1 report. Sum rates when people work together; multiply by time to get completed fraction. Remainder divided by the later combined rate gives the additional time needed.

Step-by-Step Solution:

Verification / Alternative check:As a quick reasonableness check, A contributes 4*(1/16)=1/4. B and C together at 11/120 per hour need about (3/4)/(11/120) ≈ 8.18 hours if A never came; but A contributed more than 1/4 because everyone worked initially; our precise arithmetic above gives 5:11 p.m., which is consistent.

Why Other Options Are Wrong:04:10 p.m.: underestimates remaining time after A leaves.05:45 p.m.: overestimates B+C time.06:15 p.m.: significantly longer than required by computed remainder and rate.

Common Pitfalls:Mixing average time with sum of times; not converting to per-hour rates; rounding too early; or assuming integer minutes. Keep exact fractions until the end.

Final Answer:05:11 p.m.