Question

Secretariat is known as the horse with the fastest run in the Kentucky Derby. If Secretariat's record 1.25 -mi run lasted 1 minute 59.2 seconds, what was his average speed in \(\mathrm{m} / \mathrm{s} ?\)

Short answer

Secretariat's average speed during his record 1.25-mile run was approximately 16.879 meters per second.

Step-by-step solution

Convert distance from miles to meters

We are given the distance as 1.25 miles. To convert miles to meters, we can use the conversion factor: 1 mile = 1,609.34 meters. Therefore, we have: \(1.25 \ \text{miles} \times 1,609.34 \ \dfrac{\text{meters}}{\text{mile}} = 2,011.675 \ \text{meters}\) The distance is approximately 2,011.675 meters.

Convert time from minutes and seconds to seconds

We are given the time as 1 minute 59.2 seconds. To convert this to seconds, we can do the following: \(1 \ \text{minute} \times 60 \ \dfrac{\text{seconds}}{\text{minute}} + 59.2 \ \text{seconds} = 60 \ \text{seconds} + 59.2 \ \text{seconds} = 119.2 \ \text{seconds}\) The time is 119.2 seconds.

Calculate average speed

To find the average speed, we can use the formula: \(\text{Average Speed} = \dfrac{\text{Distance}}{\text{Time}}\) Now, let's plug in the given values and find the average speed: \(\text{Average Speed} = \dfrac{2,011.675 \ \text{meters}}{119.2 \ \text{seconds}} ≈ 16.879 \ \text{m/s}\) Secretariat's average speed during his record 1.25-mile run was approximately 16.879 meters per second.

Key concepts

Unit Conversion

Unit conversion is an essential part of solving problems that involve different measurement systems. In everyday life, we often encounter situations where we need to convert one unit to another to understand quantities better or to perform calculations efficiently. For instance, in the exercise about Secretariat's record run in the Kentucky Derby, we needed to convert units from miles to meters. To do this, we use a conversion factor. In this case, the conversion factor between miles and meters is 1 mile = 1,609.34 meters. So, by multiplying the distance in miles by the conversion factor, we change the unit from miles to meters.

• 1.25 miles x 1,609.34 meters/mile = 2,011.675 meters

This process is straightforward once you identify the correct conversion factors. Remember, converting units correctly sets the foundation for accurate calculations later in the problem-solving process.

Distance and Time

Understanding the relationship between distance and time is crucial for calculating speed. Speed is defined as the rate at which an object covers distance over a period of time. In the exercise, Secretariat's run necessitates finding his average speed, which is computed using distance and time.To begin, the given time of the run is 1 minute and 59.2 seconds. To convert this into seconds (because we want speed in meters per second), we take:

• 1 minute = 60 seconds
• 1 minute 59.2 seconds = 60 + 59.2 = 119.2 seconds

Next, we use the formula for average speed, which is:\[\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}\]This conversion ensures our units align correctly for calculating average speed as meters per second.

Kentucky Derby

The Kentucky Derby is a famous annual horse race in the United States. It takes place in Louisville, Kentucky, and is renowned for being the most prestigious horse race in the country. Known as "The Run for the Roses," it features thoroughbred horses running a distance of 1.25 miles or approximately 2,011.675 meters. Racers and spectators from around the world gather to witness the event, which highlights both the horses' speed and endurance. Beyond the excitement of the race, it also offers a practical application for exercising mathematical concepts. Understanding how to compute a horse's average speed involves real-life unit conversions and timed distances. Secretariat, a legendary racehorse, holds the record for the fastest run in the Kentucky Derby, illustrating how these mathematical concepts help quantify his amazing achievement efficiently.