The height of water in Tank A over time follows the linear function \(\mathrm{h(t) = 2.5t + 15}\), where h...

1. TRANSLATE the problem information

• Given information:
  • Tank A: \(\mathrm{h(t) = 2.5t + 15}\) (height in inches, time in hours)
  • Tank B changes at the same rate as Tank A
• Need to find: Rate of change for Tank B in inches per hour

2. INFER the mathematical meaning of rate of change

• In the linear function \(\mathrm{h(t) = 2.5t + 15}\):
  • This is in the form \(\mathrm{h(t) = mt + b}\)
  • The coefficient of t (which is 2.5) represents the rate of change
  • The constant term (15) represents the starting height

3. INFER the connection between the tanks

• Tank A's rate of change = 2.5 inches per hour
• Since Tank B "changes at the same rate" as Tank A
• Tank B's rate of change = 2.5 inches per hour

Answer: A) 2.5

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Confusing the y-intercept with the rate of change

Students see the function \(\mathrm{h(t) = 2.5t + 15}\) and focus on the larger number (15), thinking this represents how fast the water level changes. They don't recognize that in linear functions, the coefficient of the variable represents the rate of change, not the constant term.

This may lead them to select Choice C (15.0)

Second Most Common Error:

Poor TRANSLATE reasoning: Misunderstanding "same rate" to mean addition

Students think that if Tank B changes at the same rate as Tank A, they need to somehow combine the values 2.5 and 15, leading them to calculate \(\mathrm{2.5 + 15 = 17.5}\).

This may lead them to select Choice D (17.5)

The Bottom Line:

Success on this problem requires recognizing that linear functions encode rate of change in their coefficient, not in their constant term. The key insight is that "rate of change" and "slope" are the same concept in linear relationships.