Combined work rate when both work: \(\frac{1}{12} + \frac{1}{15} = \frac{5+4}{60} = \frac{9}{60} = \frac{3}{20}\)

["Combined Work Rate: When Two Workers Work Together – Solved and Explained", "When tackling projects or assignments, understanding how different workers contribute over time is essential — especially when combining their efforts. One common scenario in work-rate problems is determining the combined work rate when two people work simultaneously. A classic example involves calculating total output when two workers have individual rates given as fractions of work completed per hour.", "### Understanding Work Rates", "Work rate is defined as the fraction of work completed in one unit of time — typically per hour. If a task can be fully completed in 12 hours, that worker’s work rate is (\frac{1}{12}) of the job per hour. Likewise, a worker finishing the same task in 15 hours has a rate of (\frac{1}{15}) per hour.", "When two workers collaborate, their combined work rate is the sum of their individual rates. This principle assumes both workers contribute continuously and independently to the task.", "### Example Problem: Combined Work Rate", "Consider two workers with known work rates:", "- Worker A completes (\frac{1}{12}) of the job per hour.\n- Worker B completes (\frac{1}{15}) of the job per hour.", "To find how fast they finish the job together, compute their combined rate:", "[\n\ ext{Combined rate} = \frac{1}{12} + \frac{1}{15}\n]", "### Step-by-Step Calculation", "Step 1: Find a common denominator\nThe least common denominator (LCD) of 12 and 15 is 60.", "Convert both fractions:", "[\n\frac{1}{12} = \frac{5}{60}, \quad \frac{1}{15} = \frac{4}{60}\n]", "Step 2: Add the fractions\n[\n\frac{5}{60} + \frac{4}{60} = \frac{9}{60}\n]", "Step 3: Simplify the result\n[\n\frac{9}{60} = \frac{3}{20}\n]", "### Final Interpretation", "The combined work rate of the two workers is (\frac{3}{20}) of the job completed per hour. This means together, they finish (\frac{3}{20}) of the task each hour, which directly informs how long it will take to complete the full project.", "### Time to Complete the Job", "To determine total time (T) needed to finish the job:", "[\nT = \frac{1}{\ ext{Combined rate}} = \frac{1}{\frac{3}{20}} = \frac{20}{3} \ ext{ hours} \approx 6.67 \ ext{ hours}\n]", "### Why This Approach Matters", "Understanding combined work rates applies across engineering, project management, and daily productivity scenarios. By converting work into fractions, we simplify complex labor contributions into manageable arithmetic, enabling quick decisions and accurate planning.", "### Conclusion", "Combined work rate is a powerful concept in time-and-work problems. Using simple fractions — like in (\frac{1}{12} + \frac{1}{15} = \frac{3}{20}) — transforms individual efforts into a unified, powerful force. Recognize this formula whenever multiple workers or machines collaborate — faster completion is always on the horizon.", "---", "Keywords: combined work rate, work rate calculation, fraction addition, teamwork and productivity, time and work problems, math for work efficiency, fraction work rates, project time estimation", "Meta description: Learn how to calculate combined work rate when two workers work together. Solve problems like (\frac{1}{12} + \frac{1}{15} = \frac{3}{20}) using LCD and fractions to find efficient team productivity."]