On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?
1. TRANSLATE the problem information
- Given information:
- Distance: 11 miles
- Time: 26 minutes
- Find: average speed in miles per hour
2. INFER the approach
- We need the average speed formula: \(\mathrm{speed = distance \div time}\)
- But there's a unit mismatch: we have minutes but need miles per hour
- Strategy: First find speed in miles per minute, then convert to miles per hour
3. SIMPLIFY to find speed in miles per minute
- Average speed = \(\mathrm{11\, miles \div 26\, minutes = 11/26}\) miles per minute
4. INFER the unit conversion needed
- To convert miles per minute to miles per hour, multiply by 60 (since \(\mathrm{60\, minutes = 1\, hour}\))
- This gives us: \(\mathrm{(11/26) \times 60}\) miles per hour
5. SIMPLIFY the calculation
- \(\mathrm{(11/26) \times 60 = (11 \times 60)/26 = 660/26}\)
- Calculate: \(\mathrm{660 \div 26 = 25.384615...}\) (use calculator)
- Round to nearest tenth: 25.4 miles per hour
Answer: 25.4
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students calculate \(\mathrm{11 \div 26 = 0.423...}\) and think this is the final answer, forgetting that the question asks for miles per hour, not miles per minute.
They see a small decimal like 0.42 and either select it as-is or get confused because it doesn't match typical speeds they expect for a horse. This leads to confusion and guessing.
Second Most Common Error:
Poor unit conversion execution: Students recognize they need to convert but make calculation errors, such as dividing by 60 instead of multiplying by 60, or incorrectly computing \(\mathrm{660 \div 26}\).
This may lead them to get an answer like 4.2 mph (if they divided by 60) or other incorrect values from calculation mistakes.
The Bottom Line:
This problem tests whether students can work systematically through a rate problem involving unit conversion. The key insight is recognizing that average speed problems always require matching the time units in the question with the time units in the given information.