Question

In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner.Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?

Short answer

The second-place runner beats the third-place runner by 10 feet.

Step-by-step solution

- Understand the distances involved

The winner finishes 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. We need to find out how many feet the second-place runner beats the third-place runner by.

- Calculate the relative distance between the second and third runners

Since the winner is 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner, the difference in distances between the second-place runner and the third-place runner is 20 feet - 10 feet = 10 feet.

- Conclusion

The second-place runner beats the third-place runner by 10 feet.

Key concepts

Relative Distance

In races, relative distance refers to how far apart the runners are from each other. This helps to determine their positions in the race. For example, in a 1-mile race where the winner finishes 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner, understanding relative distance becomes important.
To find the distance by which the second-place runner beats the third-place runner, you look at the differences in distance from the winner. Here, the difference is calculated by subtracting the 10 feet (distance between the winner and the second-place runner) from the 20 feet (distance between the winner and the third-place runner). So, 20 - 10 = 10 feet. Thus, the second-place runner is 10 feet ahead of the third-place runner.

If you grasp this concept of relative distance, it makes understanding race outcomes easier.

Constant Speed

In the context of a race, when we say that runners maintain a constant speed, it means they run at a steady pace throughout the race. This simplifies calculating their positions at any given point in time.
For instance, if the winner, the second-place runner, and the third-place runner all maintain constant speeds, their distances from each other remain consistent. This is why, in our original example, the relative distance calculation holds true.
Understanding constant speed can help simplify the math involved in determining race outcomes. If a runner’s speed fluctuates, it would be much more complex to make precise calculations about their positions relative to other runners.

Race Outcome Analysis

Analyzing race outcomes involves looking at the concluding positions and distances between runners. This helps us understand their performance in relation to each other.
In our exercise, the simple race outcome analysis reveals the following:

• The winner finishes first, 10 feet ahead of the second-place runner.
• The second-place runner comes in 10 feet ahead of the third-place runner.
• The third-place runner is 20 feet behind the winner, meaning they are the furthest behind.

By breaking these distances down, we gain a clearer picture of the race dynamics.
Race outcome analysis is pivotal for not only understanding who won but also by what margin. It offers deeper insights into each runner’s performance and consistency.
Remember, having a clear understanding of concepts like relative distance and constant speed enhances your ability to analyze race outcomes effectively.