P = W/tThe power P produced by a machine is represented by the equation above, where W is the work...

1. TRANSLATE the problem requirements

• Given equation: \(\mathrm{P = W/t}\)
• Goal: Express \(\mathrm{W}\) in terms of \(\mathrm{P}\) and \(\mathrm{t}\) (isolate \(\mathrm{W}\) on one side)

2. INFER the solution strategy

• \(\mathrm{W}\) is currently divided by \(\mathrm{t}\) in a fraction
• To isolate \(\mathrm{W}\), I need to eliminate the division by \(\mathrm{t}\)
• Since division and multiplication are inverse operations, I should multiply both sides by \(\mathrm{t}\)

3. SIMPLIFY through algebraic manipulation

• Multiply both sides of \(\mathrm{P = W/t}\) by \(\mathrm{t}\):
  - Left side: \(\mathrm{P \times t = Pt}\)
  - Right side: \(\mathrm{(W/t) \times t = W}\)
• Result: \(\mathrm{Pt = W}\), or equivalently \(\mathrm{W = Pt}\)

Answer: A. \(\mathrm{W = Pt}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what "express \(\mathrm{W}\) in terms of \(\mathrm{P}\) and \(\mathrm{t}\)" means and attempt random algebraic manipulations instead of systematically isolating \(\mathrm{W}\).

They might try operations like dividing both sides by \(\mathrm{t}\) or adding \(\mathrm{t}\), leading to incorrect relationships. This confusion about the goal causes them to select wrong manipulations and potentially choose Choice B (\(\mathrm{W = P/t}\)) or Choice D (\(\mathrm{W = P + t}\)).

Second Most Common Error:

Poor INFER reasoning: Students recognize they need to isolate \(\mathrm{W}\) but choose the wrong operation - they might divide both sides by \(\mathrm{t}\) instead of multiplying, or confuse the order of operations needed.

This leads them to create expressions like \(\mathrm{W = P/t}\) by incorrectly thinking "if \(\mathrm{P = W/t}\), then \(\mathrm{W = P/t}\)" without proper algebraic justification. This may lead them to select Choice B (\(\mathrm{W = P/t}\)).

The Bottom Line:

This problem tests fundamental equation-solving skills. Success requires clearly understanding the goal (isolate \(\mathrm{W}\)) and systematically applying inverse operations. Students who struggle often either misunderstand what they're solving for or apply operations incorrectly.