Work Rate Problems

Calculate time or workers needed when the total work stays constant.

Learn

Calculate time or workers needed when the total work stays constant.

Work rate problems are based on the formula: Work = Rate × Time, or equivalently, Work = Workers × Days. If the total work is constant, increasing workers decreases time proportionally. The key insight is that 'worker-days' (or 'machine-hours') represents the total work, and this stays the same regardless of how many workers do the job.

Total Work = Workers × Time. If W1 × T1 = W2 × T2, then T2 = (W1 × T1) / W2

4 workers in 12 days = 48 worker-days. 6 workers = 48 ÷ 6 = 8 days
3 machines in 10 hours = 30 machine-hours. 5 machines = 30 ÷ 5 = 6 hours
2 people in 15 days = 30 person-days. 5 people = 30 ÷ 5 = 6 days

How to recognize it

Problem mentions workers/machines and time to complete a job
Asks how long with different number of workers
Total work (job size) remains constant

Common mistakes

Thinking more workers means more time (it's inverse)
Adding workers instead of multiplying
Forgetting that work = workers × time

Step-by-step walkthrough

5 workers can complete a project in 12 days. How many days would it take 10 workers?

Calculate total work in worker-days: 5 workers x 12 days = 60 worker-days
The total work stays constant at 60 worker-days
Divide total work by new number of workers: 60 / 10 workers
Calculate: 60 / 10 = 6 days

Answer: 6 days

Practice guidance

Numerical Reasoning