Alternate Work
Alternate work problems explore workflows where team members take turns on a project rather than working simultaneously. Solving these requires tracking performance over complete rotational blocks.
Fundamental Principles
Cyclical Time Block
The combined time period required for every individual in the rotation to complete exactly one active shift (e.g., a 2-day block if two workers alternate days).
Fractional Remainder Shift
The final pieces of uncompleted work left over after the last full rotation cycle, which must be assigned to whoever is next up in the queue.
Essential Formulation Tips
- Always identify exactly who starts the first shift, as the order of rotation directly dictates who handles the final remainder steps.
- Avoid using standard combined formulas directly; instead, calculate the specific work completed per multi-day cycle.
Shortcut Execution Techniques
- Find the total work completed in one full multi-day cycle, then use integer division to find how many full cycles fit into the total project pool. This reveals the remaining work instantly.
Contextual Inquiries (FAQs)
Q:
A:
Q:
A:
Example Breakdown: Two-Agent Alternating Shift Matrix
Classic rotational tracking application often featured on competitive exams.Step 1: Establish the total work pool using the LCM of 10 and 20: 20 units.
Step 2: Find daily efficiencies: Alan = 2 units/day; Brian = 1 unit/day.
Step 3: Analyze one full 2-day cycle: Day 1 (Alan) adds 2 units + Day 2 (Brian) adds 1 unit = 3 units per cycle.
Step 4: Scale the cycles up close to the target: 6 full cycles × 3 units = 18 units completed over 12 days.
Step 5: Process the remaining work: 2 units left (20 - 18). Alan handles Day 13 and completes exactly 2 units.
Step 6: Sum the total timeline: 12 days + 1 full day = 13 days.
Alternate Work Practice Set 1
10 scenario matrices looking at three-person rotations, changing start orders, and partial shifts.
Q1. A and B work alternating days. A can finish the job in 9 days, and B can finish it in 12 days. If A starts on Day 1, exactly how long does the job take?
Q2. Refer to the question above: If B starts on Day 1 instead of A, how many days will the same job take?