A and B together finish a job in 30 days. A works alone for 16 days; B then finishes the remainder alone in 44 days. In how many days can B alone finish the whole job?

Problem restatement
We know the joint time for (A + B), a head start by A, and the finishing time by B alone. Find B's solo time.

Given data

• a + b = 1/30 (job/day).
• A works 16 days alone: work = 16a.
• B finishes the rest in 44 days: 44b = 1 − 16a.

Concept/Approach
Express a = 1/30 − b and substitute into the remainder equation to solve for b.

Step-by-step calculation
44b = 1 − 16(1/30 − b) = 1 − 16/30 + 16b = 1 − 8/15 + 16b = 7/15 + 16b 44b − 16b = 7/15 → 28b = 7/15 → b = 1/60 Therefore, B's time = 1 ÷ b = 60 days

Verification
Then a = 1/30 − 1/60 = 1/60; A's 16 days produce 16/60 = 4/15 of the job; remainder 11/15 finished by B in 44 days → 44 × (1/60) = 11/15 (consistent).

Common pitfalls

• Using 30 − 16 − 44 style arithmetic on days (invalid); must use rates and work.

Final Answer
60 days