A runner wants to run 10.0 km. Her running pace is 7.5 mi per hour. How many minutes must she run?

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Convert the distance from kilometers to miles using the conversion factor: 1 km = 0.621371 miles.

Calculate the total distance in miles by multiplying 10.0 km by the conversion factor.

Determine the time in hours by dividing the distance in miles by the runner's pace in miles per hour (7.5 mi/h).

Convert the time from hours to minutes by multiplying the time in hours by 60 minutes per hour.

The result is the number of minutes the runner must run to cover 10.0 km.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, the runner's pace is given in miles per hour, while the distance to be covered is in kilometers. To solve the problem, it is essential to convert either the pace to kilometers per hour or the distance to miles to ensure both measurements are in compatible units.

Speed and Time Relationship

The relationship between speed, distance, and time is defined by the formula: speed = distance/time. This means that time can be calculated by rearranging the formula to time = distance/speed. Understanding this relationship is crucial for determining how long it will take the runner to complete the 10.0 km distance at her given pace.

Pace Calculation

Pace is typically expressed as the time taken to cover a certain distance, often in minutes per mile or minutes per kilometer. In this scenario, converting the runner's speed into a pace format will help in calculating the total time required to run 10.0 km. Knowing how to convert speed into pace is essential for solving the problem accurately.

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