A machine produces widgets at a constant rate of 15 widgets per hour. At this rate, what is the time,...

1. TRANSLATE the problem information

• Given information:
  • Production rate: 15 widgets per hour
  • Total widgets needed: 225 widgets
  • Find: Time required in hours

2. INFER the mathematical relationship

• Since we know rate and total amount, we need to find time
• The fundamental relationship is: \(\mathrm{Amount = Rate \times Time}\)
• Rearranging to solve for time: \(\mathrm{Time = Amount \div Rate}\)

3. SIMPLIFY by performing the calculation

• \(\mathrm{Time = 225\ widgets \div 15\ widgets\ per\ hour}\)
• \(\mathrm{Time = 15\ hours}\)

Answer: A (15)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse multiplication and division in rate problems

Instead of recognizing they need to divide total by rate, they multiply: \(\mathrm{225 \times 15 = 3,375}\). This may lead them to select Choice D (3375).

The Bottom Line:

Rate problems require careful attention to what operation connects the three quantities (rate, time, total). When you know rate and total amount, division gives you the time.