Which of the following speeds is equivalent to 90 kilometers per hour? 1text{ kilometer} = 1{,}000text{ meters}

1. TRANSLATE the problem information

• Given information:
  • Speed: \(\mathrm{90\text{ kilometers per hour}}\)
  • Conversion factor: \(\mathrm{1\text{ kilometer} = 1{,}000\text{ meters}}\)
  • Need to find: equivalent speed in meters per second

2. INFER the approach

• This is a unit conversion problem where both distance and time units need converting
• Strategy: Convert the numerator (kilometers → meters) and denominator (hours → seconds) separately, then calculate the new rate

3. SIMPLIFY the distance conversion

• Convert kilometers to meters:
  \(\mathrm{90\text{ kilometers} \times 1{,}000\text{ meters/kilometer} = 90{,}000\text{ meters}}\)

4. SIMPLIFY the time conversion

• Convert hours to seconds:
  • \(\mathrm{1\text{ hour} = 60\text{ minutes}}\)
  • \(\mathrm{1\text{ minute} = 60\text{ seconds}}\)
  • Therefore: \(\mathrm{1\text{ hour} = 60 \times 60 = 3{,}600\text{ seconds}}\)

5. SIMPLIFY to find the final rate

• Calculate: \(\mathrm{90{,}000\text{ meters} \div 3{,}600\text{ seconds} = 25\text{ meters per second}}\)

Answer: A. 25 meters per second

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students often convert only one unit instead of recognizing both distance and time units need conversion. For example, they might convert 90 kilometers to 90,000 meters but forget that "per hour" also needs to be converted to "per second." This incomplete conversion leads to answers like 90,000 meters per hour, causing confusion about which answer choice to select.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up the conversion but make arithmetic errors in calculating \(\mathrm{90{,}000 \div 3{,}600}\). Common mistakes include getting 250 (forgetting to account for the full 3,600 divisor) or 32 (calculation errors). This may lead them to select Choice C (250 meters per second) or Choice B (32 meters per second).

The Bottom Line:

This problem requires systematic thinking about unit conversion - recognizing that "per" creates a fraction where both numerator and denominator units may need converting. Students who try shortcuts or convert only partial units will select incorrect answers.