A train travels at a constant speed for 2 hours, covering a total distance of 140 miles. What is the...

1. TRANSLATE the problem information

• Given information:
  • Distance traveled = 140 miles
  • Time traveled = 2 hours
  • Need to find: Speed in miles per hour

2. INFER the approach

• We need to use the relationship between distance, speed, and time
• Since we know distance and time, we can find speed
• The formula \(\mathrm{Distance = Speed \times Time}\) needs to be rearranged to solve for Speed

3. Set up the equation

• \(\mathrm{Distance = Speed \times Time}\)
• \(\mathrm{140 = Speed \times 2}\)

4. SIMPLIFY to solve for speed

• Divide both sides by 2:
  \(\mathrm{Speed = 140 \div 2}\)
  \(\mathrm{Speed = 70}\)

Answer: 70 miles per hour

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse which values go where in the formula, mixing up what represents distance, speed, and time from the word problem.

They might incorrectly think speed is 2 and try to solve for time or distance, leading to confusion about what the problem is actually asking for. This leads to setting up incorrect equations and getting stuck.

Second Most Common Error:

Missing conceptual knowledge: Students don't remember the distance-speed-time relationship formula or confuse it with other formulas.

Without knowing that \(\mathrm{Distance = Speed \times Time}\), they can't set up the problem correctly and may resort to guessing or using incorrect relationships. This causes them to get stuck and guess.

The Bottom Line:

This problem tests whether students can recognize a basic distance-speed-time situation and translate it into the correct mathematical setup. The arithmetic is straightforward once the setup is correct.