A can do a job in 30 days and B can do the same job in 40 days. How many days will they take to finish the job when working together?

Introduction / Context: When two workers combine, their rates add. Convert individual times to rates, add, and invert to get the combined time.

Given Data / Assumptions:

• A alone = 30 days ⇒ r(A) = 1/30 per day.
• B alone = 40 days ⇒ r(B) = 1/40 per day.

Concept / Approach: Combined rate r = 1/30 + 1/40. Combined time T = 1 / r.

Step-by-Step Solution: 1/30 + 1/40 = (4 + 3) / 120 = 7/120. T = 1 / (7/120) = 120/7 = 17 1/7 days.

Verification / Alternative check: 17 1/7 × 7/120 = 1, confirming correctness.

Why Other Options Are Wrong: 70, 42 3/4, 27 1/7, 24 days are inconsistent with the exact combined-rate inversion.

Common Pitfalls: Averaging times (35 days) instead of adding rates; arithmetic slips in fraction handling.

Final Answer: 17 1/7 days