s = 40 + 3t. The equation gives the speed s, in miles per hour, of a certain car t...

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{s = 40 + 3t}\)
  • s represents speed in miles per hour
  • t represents time in seconds after acceleration began
  • Need to find speed when \(\mathrm{t = 5}\) seconds

2. INFER the solution strategy

• Since we have an equation relating s and t, and we know \(\mathrm{t = 5}\), we need to substitute this value into the equation
• This will give us the speed at that specific time

3. Substitute and calculate

• Replace t with 5 in the equation:
  \(\mathrm{s = 40 + 3(5)}\)
• Calculate:
  \(\mathrm{s = 40 + 15 = 55}\)

Answer: D. 55

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak arithmetic execution: Students correctly set up \(\mathrm{s = 40 + 3(5)}\) but make calculation errors

• Some might calculate \(\mathrm{3(5) = 8}\) instead of 15
• Others might add incorrectly: \(\mathrm{40 + 15 = 53}\) or similar errors

This may lead them to select Choice B (43) or Choice C (45)

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand which variable to substitute or what the equation represents

• Some might substitute 5 for s instead of t
• Others might add just 3 instead of 3(5), getting \(\mathrm{40 + 3 = 43}\)

This may lead them to select Choice B (43)

The Bottom Line:

This problem tests whether students can correctly interpret a linear function and substitute values accurately. The key is recognizing that \(\mathrm{t = 5}\) goes into the equation, then performing the arithmetic correctly.