An object travels at a constant speed of 12 centimeters per second. At this speed, what is the time, in...

1. TRANSLATE the problem information

• Given information:
  • Speed: \(12\) centimeters per second
  • Distance to travel: \(108\) centimeters
  • Find: time in seconds

2. INFER the approach

• We need to use the distance-speed-time relationship
• Since we know distance and speed, we need to solve for time
• The formula \(\mathrm{distance} = \mathrm{speed} \times \mathrm{time}\) must be rearranged to: \(\mathrm{time} = \mathrm{distance} \div \mathrm{speed}\)

3. SIMPLIFY by calculating

• \(\mathrm{time} = 108 \text{ cm} \div 12 \text{ cm/s}\)
• \(\mathrm{time} = 9 \text{ seconds}\)

Answer: A. 9

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students recognize this involves distance, speed, and time but don't properly identify which operation to use. Instead of dividing distance by speed, they may add the two numbers together.

This leads them to calculate \(108 + 12 = 120\), causing them to select Choice C (120).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret what the problem is asking and perform subtraction, thinking they need to find some kind of difference.

This leads them to calculate \(108 - 12 = 96\), causing them to select Choice B (96).

The Bottom Line:

The key challenge is recognizing that "how long does it take" requires dividing the distance by the speed, not performing other arithmetic operations with the given numbers.