When one grows and the other shrinks
6 people painted a hall in 12 days. How long would 8 people take?
- 4 people, 18 days.
- 6 people, 12 days — same area.
- 12 people, 6 days — same area again.
- Every rectangle covers 72.
If everyone works at the same speed, 8 people take 9 days.
Each rectangle has sides of people and days. Its area is people × days. A product is the answer to a multiplication.
Rule: Two amounts are in inverse proportion when their product stays fixed. Here, people × days makes 72, when everyone works at the same speed.
The product 6 × 12 = 72 stays fixed. So 8 people take 72 ÷ 8 = 9 days, not 10. People rose by 2. Days fell by 3, not 2. The product stays fixed, not the difference.
Watch out!
A number that falls is not always inverse. A tank holds 200 litres (L). It drains at 20 L a minute. After 1 minute it holds 180 L. After 2 minutes it holds 160 L. But 1 × 180 and 2 × 160 differ. Test the product on every row.
Tap More people or Fewer people. Watch the box.
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