Answer First
Taylor ran 30 miles. This comes from multiplying 7.5 hours by 4 miles per hour (7.5 × 4 = 30).
Understanding the Question
The question gives two key facts: a time of seven and a half hours and an average speed of four miles per hour. It asks for the total distance covered. To find distance, multiply time by speed. Here, 7.5 hours × 4 miles per hour equals 30 miles. The reasoning is straightforward: when speed stays roughly steady, distance is the product of time and rate.
Core Concept: Distance Formula
The basic relationship among distance, rate, and time is expressed as distance equals rate multiplied by time (d = r × t). In this scenario, rate is 4 miles per hour and time is 7.5 hours. Plugging these values into the formula gives d = 4 × 7.5, which simplifies to 30. This formula is a cornerstone of motion problems and applies whenever average speed remains consistent over a given period.
Units and Meaning
Multiplying hours by miles per hour cancels the time unit, leaving miles. Specifically, 4 miles per hour for 7.5 hours means covering four miles in each full hour, plus half of that hour’s distance (2 miles), totaling 30 miles. Understanding unit cancellation helps confirm that the operation and the answer are consistent.
Step-by-Step Calculation
Follow these steps to solve similar problems reliably.
- Convert time to a single unit: 7.5 hours is already in hours, so no conversion is needed.
- Identify average speed: 4 miles per hour.
- Apply the formula: Distance = 4 × 7.5.
- Compute: 4 × 7 = 28, and 4 × 0.5 = 2; 28 + 2 = 30.
- State the result with correct units: 30 miles.
Practical Context for Endurance Training
In distance training, maintaining a steady pace helps estimate total work. Running 30 miles at 4 mph would typically take about 7.5 hours. This gives athletes a way to plan long runs, set distance goals, and track progress over time. Coaches and runners often use these calculations to structure training cycles and ensure gradual increases in mileage.
Comparison With Common Road Distances
It can be helpful to compare 30 miles with familiar benchmarks. Standard road races and training runs provide useful reference points for understanding this distance.
| Distance | Common Context | Typical Duration at 4 mph |
|---|---|---|
| 5K (3.1 miles) | Popular fun run length | About 47 minutes |
| 10K (6.2 miles) | Common competitive race | About 1 hour 33 minutes |
| Half Marathon (13.1 miles) | Major milestone for runners | About 3 hours 15 minutes |
| 30 miles | Taylor’s total distance | 7.5 hours |
| Marathon (26.2 miles) | Classic endurance event | About 6 hours 30 minutes |
Why Accurate Calculation Matters
Getting the multiplication correct supports training plans, race strategy, and logistics. Misestimating distance can affect hydration, nutrition, and scheduling. By applying the distance formula consistently, you reduce errors and make informed decisions for workouts and events.
Applying This to Other Problems
The same method works for other scenarios: if time or speed changes, adjust one variable at a time. For example, running 5 hours at 4 mph would be 20 miles; running 7.5 hours at 5 mph would be 37.5 miles. Practicing these variations reinforces the concept and builds confidence in using d = r × t.
Reliable Problem-Solving Approach
Use a clear, repeatable process: identify given values, write the formula, substitute numbers, compute carefully, and label units. This approach not only answers the question at hand but also equips you to handle similar problems with accuracy. For Taylor, the result is 30 miles—a concrete outcome derived from simple, dependable math.
Key Takeaways
- Distance equals rate multiplied by time (d = r × t).
- 7.5 hours at 4 mph yields 30 miles.
- Unit analysis (hours cancel) confirms the operation.
- Useful for planning training and understanding effort.
- Cross-check with known distances to validate reasonableness.
