A delivery route consists of a 4-mile urban segment and a 10-mile highway segment traveled consecutively. The total time for...
GMAT Algebra : (Alg) Questions
A delivery route consists of a 4-mile urban segment and a 10-mile highway segment traveled consecutively. The total time for the route is 0.6 hours, where each segment is traveled at a constant average speed. The equation \(\frac{4}{\mathrm{x}} + \frac{10}{\mathrm{y}} = 0.6\) represents this situation. Which of the following is the best interpretation of x in this context?
- The average speed on the urban segment, in miles per hour
- The average speed on the highway segment, in miles per hour
- The time to traverse the urban segment, in hours
- The time to traverse the highway segment, in hours
1. TRANSLATE the problem information
- Given information:
- 4-mile urban segment + 10-mile highway segment
- Total time: 0.6 hours
- Equation: \(\frac{4}{x} + \frac{10}{y} = 0.6\)
- Each segment traveled at constant speed
2. INFER the equation structure
- The equation adds two terms to equal total time
- This suggests each term represents time for one segment
- Since time = distance ÷ speed, each fraction follows this pattern
3. TRANSLATE each term in the equation
- First term: \(\frac{4}{x}\)
- 4 = distance of urban segment (4 miles)
- x = what we divide distance by to get time
- Therefore: x = speed of urban segment
- Second term: \(\frac{10}{y}\)
- 10 = distance of highway segment (10 miles)
- y = speed of highway segment
4. INFER the correct interpretation
- Since x appears in the denominator of the urban segment fraction
- And distance ÷ speed = time
- x must represent the average speed on the urban segment in miles per hour
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may focus on what each term equals (time) rather than what the variables represent within each term.
They might think: "\(\frac{4}{x}\) gives me time for the urban segment, so x must be time too." This confuses the variable with what the expression equals, leading them to select Choice C (The time to traverse the urban segment, in hours).
Second Most Common Error:
Inadequate INFER reasoning: Students may not connect the equation structure to the distance/speed/time relationship.
Without recognizing that the equation follows time = distance/speed format, they might guess based on position in the equation rather than mathematical meaning. This leads to confusion and guessing between the remaining choices.
The Bottom Line:
Success requires recognizing that when distance is divided by a variable to get time, that variable must represent speed. The key insight is understanding what role each component plays in the distance/speed/time relationship.