An object travels at a constant speed of 6 centimeters per second. At this speed, what is the time, in...

1. TRANSLATE the problem information

• Given information:
  • Speed = 6 centimeters per second
  • Distance to travel = 24 centimeters
• What we need to find: time in seconds

2. INFER the approach

• This is a distance-rate-time problem
• We can use the relationship: \(\mathrm{Distance = Rate \times Time}\)
• Since we know distance and rate, we can solve for time: \(\mathrm{Time = Distance \div Rate}\)

3. SIMPLIFY to find the answer

• \(\mathrm{Time = 24\ centimeters \div 6\ centimeters\ per\ second}\)
• \(\mathrm{Time = 4\ seconds}\)

Answer: 4

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse what values they have versus what they need to find, or mix up the relationship between distance, rate, and time.

Some students might incorrectly calculate \(\mathrm{6 \times 24 = 144}\), thinking they need to multiply the rate by the distance instead of dividing distance by rate. This leads to confusion and guessing since 144 won't match any reasonable answer for seconds.

Second Most Common Error:

Poor INFER reasoning: Students might not recognize the fundamental relationship between distance, rate, and time, or may not know how to rearrange the formula.

Without understanding that \(\mathrm{Time = Distance \div Rate}\), they may attempt random operations with the given numbers, leading to incorrect calculations and answer selection.

The Bottom Line:

The key challenge is recognizing this as a distance-rate-time problem and correctly applying the relationship that time equals distance divided by rate. Students who memorize formulas without understanding the underlying relationships often struggle with determining which operation to use.