Time and Work: A and B | Dataford Interview Questions

Your question is Time and Work: A and B. Start with the requirements on the right.

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Problem

Systems Planning and Analysis is estimating the duration of a shared planning task. Contributor A can complete the task alone in a_days days, while contributor B can complete it alone in b_days days. Assuming they work simultaneously at constant rates, calculate the number of days required when they work together.

Implement combined_work_days(a_days, b_days).

Formal Specification

Input: Two positive numbers, a_days and b_days, representing the individual completion times in days.
Output: A floating-point number representing the combined completion time in days.
The result should be accurate within 1e-9 of the mathematically correct value.

Each contributor's daily work rate is the reciprocal of their individual completion time. The combined rate is the sum of those two rates, so the completion time is the reciprocal of the combined rate.

Constraints

1 <= a_days, b_days <= 10^9
Both inputs are positive numbers
Work rates are constant
The result is judged with floating-point tolerance of 1e-9

Function Signature

def combined_work_days(a_days, b_days):