Helper joins mid-way on a construction task A mason can build a tank in 12 hours. He works alone for 6 hours, then a boy helps and they finish the job in 5 more hours. How long would the boy take to complete the entire job alone?

Introduction / Context:
When a helper joins partway, compute the initial portion done by the first worker, then infer the combined rate to deduce the helper’s individual rate.

Given Data / Assumptions:

• Mason completes job in 12 h ⇒ rate = 1/12 per hour.
• Mason works alone for 6 h ⇒ completes 1/2 of the job.
• Remaining 1/2 is done by mason + boy in 5 h.

Concept / Approach:
Combined rate = remaining work / time. Boy’s rate = combined rate − mason’s rate. Time for boy alone = 1 / boy’s rate.

Step-by-Step Solution:

Verification / Alternative check:
In 5 hours together they do 5 * (1/10) = 1/2, which matches the remaining half.

Why Other Options Are Wrong:
45 h, 30 h, 64 h do not match the inferred boy’s rate 1/60.

Common Pitfalls:
Assuming linear sharing without first computing combined rate from the second phase.

Final Answer:
60 h