Study guides › Level 8 · Algebra 2

More workers, fewer days (inverse variation)

Level 8 · Algebra 2 · for questions like “6 painters take 10 days. How long would 4 painters take?”

💡 The idea

When one thing goes up and the other goes down so that their product stays the same, find that product first.

🪜 The steps

1. Multiply to get the total job (painter-days, or miles).
2. Divide by the new number.

✏️ Worked examples

1. 6 painters, 10 days, now 4 painters: 60 painter-days ÷ 4 = 15 days.

2. 60 mph for 4 hours, now 80 mph: 240 miles ÷ 80 = 3 hours.

⚠️ Watch out

• Sense-check: fewer workers should take longer, not less time.

🎯 Try these

1. 8 workers take 6 days. How long for 12 workers?
2. 50 mph takes 6 hours. How long at 75 mph?
3. 5 pumps take 12 hours. How long for 3 pumps?

Answers: 1) 4 days 2) 4 hours 3) 20 hours

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.