A bus is traveling at a constant speed along a straight portion of road. The equation d = 30t gives...

1. TRANSLATE the problem information

• Given information:
  • Bus equation: \(\mathrm{d = 30t}\) (\(\mathrm{d}\) = distance from marker in feet, \(\mathrm{t}\) = time in seconds after passing marker)
  • Need to find distance when \(\mathrm{t = 2}\) seconds

• What this tells us: We need to substitute \(\mathrm{t = 2}\) into the equation

2. SIMPLIFY by substituting and calculating

• Substitute \(\mathrm{t = 2}\) into \(\mathrm{d = 30t}\):
  \(\mathrm{d = 30(2)}\)
  \(\mathrm{d = 60}\)

• The bus will be 60 feet from the marker

Answer: C. 60

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the problem and substitute the wrong value for \(\mathrm{t}\)

Some students might think they need to use \(\mathrm{t = 1}\) (getting \(\mathrm{d = 30}\)) or \(\mathrm{t = 3}\) (getting \(\mathrm{d = 90}\)) instead of \(\mathrm{t = 2}\). This happens when they don't carefully read "2 seconds after passing the marker."

This may lead them to select Choice A (30) or Choice D (90)

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when calculating \(\mathrm{30(2)}\)

They might incorrectly calculate \(\mathrm{30(2)}\) as 32 instead of 60, especially if they're rushing or not being careful with basic multiplication.

This may lead them to select Choice B (32)

The Bottom Line:

This problem tests whether students can accurately read a word problem and perform substitution in a linear equation - both fundamental algebra skills that require careful attention to detail.