Test DistancesDrone P: 255 milesDrone Q: 170 milesThe table shows the distances traveled by two drones in the same amount...

1. TRANSLATE the problem information

• Given information:
  • Test flight: Drone P = 255 miles, Drone Q = 170 miles (same time)
  • New scenario: Drone P = 3,060 miles (same time duration)
  • Find: How much more does Drone P travel than Drone Q?

2. INFER the key relationship

• Since both drones fly for the same amount of time in both scenarios, their speeds stay constant
• This means the ratio of their distances must stay the same: \(255:170\)
• Whatever happens to Drone P's distance must happen proportionally to Drone Q's distance

3. Find the scaling factor

• Compare Drone P's distances: \(3{,}060 \div 255 = 12\)
• So Drone P's new distance is 12 times its test distance

4. INFER Drone Q's new distance

• Since the ratio stays constant, Drone Q's distance must also scale by factor 12
• Drone Q's new distance = \(170 \times 12 = 2{,}040\) miles

5. SIMPLIFY to find the difference

• Difference = \(3{,}060 - 2{,}040 = 1{,}020\) miles

Answer: B. 1,020

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize that the speeds maintain a constant ratio across different time periods. Instead, they might try to find the actual time or speeds, or treat this as separate, unrelated scenarios.

Without recognizing the proportional relationship, they may attempt to subtract the test distances directly (\(255 - 170 = 85\)) and select Choice A (85), not realizing this approach ignores the scaling to the new scenario.

Second Most Common Error:

Poor SIMPLIFY execution: Students understand the proportional relationship but make calculation errors when finding the scaling factor or applying it. For example, they might incorrectly calculate the scaling factor or make arithmetic errors in the final subtraction.

Calculation errors could lead them to arrive at Choice C (1,530) or Choice D (2,040), where 2,040 represents Drone Q's distance rather than the difference.

The Bottom Line:

This problem tests whether students can recognize when two scenarios are linked by proportional relationships rather than treating them as independent problems. The key insight is that constant time means constant speed ratios.