Perry, Maria, and Lorna are painting rooms in a college dormitory. Working alone, Perry can paint a standard room in...

Phase 1: Owning the Dataset

Visualization

Let's create a comparison table showing each painter's individual performance:

Key Insight

When two people work together, their rates add up. If person A has rate \(\mathrm{R_1}\) and person B has rate \(\mathrm{R_2}\), their combined rate is \(\mathrm{R_1 + R_2}\).

Phase 2: Understanding the Question

We need to find:

1. Shortest time: Which 2-person team can paint a room fastest?
2. Longest time: Which 2-person team takes the most time?

There are three possible 2-person teams:

• Perry + Maria
• Perry + Lorna
• Maria + Lorna

Phase 3: Finding the Answer

Calculating Combined Times

Team 1: Perry + Maria

• Combined rate = \(\frac{1}{180} + \frac{1}{120}\)
• Finding common denominator: \(\frac{1}{180} + \frac{1}{120} = \frac{2}{360} + \frac{3}{360} = \frac{5}{360} = \frac{1}{72}\)
• Time = 72 minutes = 1 hour 12 minutes

Team 2: Perry + Lorna

• Combined rate = \(\frac{1}{180} + \frac{1}{150}\)
• Finding common denominator: \(\frac{1}{180} + \frac{1}{150} = \frac{5}{900} + \frac{6}{900} = \frac{11}{900}\)
• Time = \(\frac{900}{11} \approx 81.8\) minutes (use calculator for precision)
• 81.8 minutes ≈ 1 hour 22 minutes

Team 3: Maria + Lorna

• Combined rate = \(\frac{1}{120} + \frac{1}{150}\)
• Finding common denominator: \(\frac{1}{120} + \frac{1}{150} = \frac{5}{600} + \frac{4}{600} = \frac{9}{600} = \frac{3}{200}\)
• Time = \(\frac{200}{3} \approx 66.7\) minutes (use calculator for precision)
• 66.7 minutes ≈ 1 hour 7 minutes

Summary of Results

Phase 4: Solution

From our calculations:

• Shortest time: Maria + Lorna at approximately 1 hour 7 minutes
• Longest time: Perry + Lorna at approximately 1 hour 22 minutes

These match exactly with the answer choices provided.