Three workers with different capacities: “A” can complete the job in 2 hours. “B” can do three times this job in 8 hours (i.e., rate = 3 jobs in 8 h). “C” can complete the same job as A in 8 hours. If all three work together on one job, how long will they take?

Introduction / Context:
The key to this problem is to translate each statement into a clear unit rate relative to the same single job. Once the individual rates are aligned (jobs per hour), they add directly. The reciprocal of the total rate gives the completion time for one job together.

Given Data / Assumptions:

• A alone: 2 hours ⇒ rate(A) = 1/2 job per hour.
• B: “thrice the work in 8 hours” ⇒ rate(B) = 3/8 job per hour.
• C: “same job as A in 8 hours” ⇒ rate(C) = 1/8 job per hour.
• All are working on one identical job together.

Concept / Approach:
Total rate = rate(A) + rate(B) + rate(C). Time = 1 / (total rate). Ensure all rates correspond to the same job, otherwise addition would be meaningless.

Step-by-Step Solution:

Verification / Alternative check:
In 1 hour, A contributes 0.5, B contributes 0.375, C contributes 0.125; sum = 1.0 job, matching the requirement.

Why Other Options Are Wrong:
2, 3, or 4 hours would imply total rates of 0.5, 0.333…, or 0.25 jobs/hour, which do not match the summed 1 job/hour capacity.

Common Pitfalls:
Misreading B’s statement as “B takes 8 hours for 1 job”; actually it is “3 jobs in 8 hours,” a faster rate than A.

Final Answer:
1 hour