More workers, fewer days: inverse proportion
A wall needs 60 worker-days of work. Change the number of workers and find how many days the job takes. Then try harvesting a field.
Core concept
When the work is fixed, the number of workers and the number of days are inversely proportional: workers × days stays the same, so twice the workers take half the days
Topic: Unitary method
Some quantities go up together: more kilograms cost more rupees (direct variation). Others go the other way: more workers finish a job in fewer days (inverse variation). If 3 workers build a wall in 20 days, the whole wall takes 3 × 20 = 60 worker-days. One worker alone would take 60 days (the unitary step). So 6 workers take 60 ÷ 6 = 10 days, and 12 workers take 5 days. The product of workers and days stays the same; that is how you recognise inverse proportion.
What you will learn
- Distinguish direct and inverse variation.
- Solve work-and-time problems with the unitary method.
- Explain why workers × days stays constant for a fixed job.
Before you start
- Know the unitary method for direct variation.
Materials
- None
Equipment
- A notebook and pencil
Procedure
- Record the wall with 3 workers.
- Record it with 6 and with 12 workers.
- Record the harvest with 5 workers.
How this simulation is simplified
- Every worker works at the same speed, and they do not get in each other's way.