Two-person team timing: A man and a boy together finish a job in 24 days. If, for the last 6 days, the man works alone and the job finishes in 26 days total, how long would the boy take alone?

Introduction / Context:
Express daily work as rates. The pair’s joint rate is known from the 24-day completion. The altered schedule provides a second equation involving the man’s solo work in the last 6 days. Solve to find each individual rate, then invert to get solo times.

Given Data / Assumptions:

• (Man + Boy) complete in 24 days ⇒ m + b = 1/24 job/day.
• In the 26-day schedule, first 20 days both work; last 6 days man works alone.

Concept / Approach:
Total work equals work in first 20 days plus work in last 6 days. Use m + b and the 26-day completion to find m, then compute b = (1/24 − m). Boy’s solo time = 1 / b days.

Step-by-Step Solution:

Verification / Alternative check:
Check rates: Together 1/24; man 1/36; boy 1/72. First 20 days: 20*(1/24) = 5/6. Last 6 days (man only): 6*(1/36) = 1/6. Total = 5/6 + 1/6 = 1 job. Valid.

Why Other Options Are Wrong:
73, 49, 62, 84 contradict the computed b = 1/72 job/day.

Common Pitfalls:
Assuming both worked for all 26 days or misallocating the last 6 days to both workers. Also, mixing times directly instead of using rates leads to errors.

Final Answer:
72 days