ISEE Upper Level Quantitative Reasoning Question of the Day

1. 288 miles
2. 324 miles (correct answer)
3. 312 miles
4. 336 miles

Explanation: This is a constant rate problem where you need to find distance using the relationship: distance = rate × time. First, calculate the train's speed using the given information. The train travels 180 miles in 2.5 hours, so its speed is $\frac{180 \text{ miles}}{2.5 \text{ hours}} = 72 \text{ miles per hour}$. Next, convert the target time to hours. Four hours and 30 minutes equals 4.5 hours (since 30 minutes = 0.5 hours). Now apply the formula: distance = rate × time = 72 mph × 4.5 hours = 324 miles. Looking at the wrong answers: Choice A (288 miles) results from incorrectly calculating the speed as 60 mph instead of 72 mph, then multiplying by 4.8 hours. Choice C (312 miles) comes from using the correct speed of 72 mph but miscalculating the time as 4.33 hours instead of 4.5 hours. Choice D (336 miles) appears when students mistakenly use 4.67 hours (4 hours and 40 minutes) instead of the correct 4.5 hours. The correct answer is B) 324 miles. Study tip: For constant rate problems, always organize your work in three steps: (1) find the rate from given information, (2) convert all times to the same units (usually hours), and (3) apply distance = rate × time. Double-check your time conversions—30 minutes is 0.5 hours, not 0.3 hours, which is a common mistake on standardized tests.