In a mechanical system, a drive gear with 60 teeth is connected to a driven gear with 20 teeth. When...

1. TRANSLATE the problem information

• Given information:
  • Drive gear: 60 teeth, 100 RPM
  • Driven gear: 20 teeth, unknown speed
  • Key constraint: "the product of the number of teeth and the rotational speed is constant for both gears"

• This constraint tells us we have an inverse proportion relationship

2. TRANSLATE the relationship into mathematical form

• The constant product relationship means:
  \(\mathrm{(Teeth_1) \times (Speed_1) = (Teeth_2) \times (Speed_2)}\)

• Substituting our known values:
  \(\mathrm{60 \times 100 = 20 \times (unknown\ speed)}\)

3. SIMPLIFY to solve for the unknown speed

• Calculate the left side:
  \(\mathrm{60 \times 100 = 6000}\)

• Our equation becomes:
  \(\mathrm{6000 = 20 \times (unknown\ speed)}\)

• Divide both sides by 20:
  \(\mathrm{unknown\ speed = 6000 \div 20 = 300\ RPM}\)

Answer: D (300)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand the inverse relationship and assume that more teeth means faster speed (direct proportion thinking).

They might reason: "The drive gear has 60 teeth and goes 100 RPM, so the driven gear with 20 teeth should go slower, maybe \(\mathrm{100 \times (20/60) = 33\ RPM}\)."

This leads them to select Choice A (33).

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up the equation but make arithmetic errors in the final calculation.

They might incorrectly calculate 6000 ÷ 20, perhaps getting 200 instead of 300, or make errors in the initial multiplication.

This may lead them to select Choice C (200).

The Bottom Line:

This problem tests whether students can correctly interpret an inverse proportion relationship in a mechanical context and avoid the intuitive (but incorrect) assumption that bigger gears always mean faster speeds.