The world's record in the 100-m dash is 9.58 s, and in the 100-yd dash it is 9.07 s. Find the speed in mi>hr of the runners who set these records. (Assume three significant figures for 100 m and 100 yd.)

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Convert the distance of 100 meters to miles. Use the conversion factor: 1 mile = 1609.34 meters.

Convert the time of 9.58 seconds to hours. Use the conversion factor: 1 hour = 3600 seconds.

Calculate the speed in miles per hour for the 100-meter dash by dividing the distance in miles by the time in hours.

Convert the distance of 100 yards to miles. Use the conversion factor: 1 mile = 1760 yards.

Calculate the speed in miles per hour for the 100-yard dash by dividing the distance in miles by the time in hours.

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Key Concepts

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

Speed Calculation

Speed is defined as the distance traveled divided by the time taken. To find the speed of the runners, we can use the formula: speed = distance/time. This calculation will yield the speed in the desired units, which in this case will be converted to miles per hour.

Unit Conversion

Unit conversion is essential when dealing with different measurement systems. In this problem, distances are given in meters and yards, which need to be converted to miles for the final speed calculation. Knowing the conversion factors, such as 1 mile = 1609.34 meters and 1 yard = 0.000568182 miles, is crucial for accurate results.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. When performing calculations, it is important to maintain the correct number of significant figures based on the values provided. In this question, the distances are given to three significant figures, which should be reflected in the final speed calculations to ensure accuracy.