Problem 47 - Prealgebra

Question

In \(2003,\) the horse Funny Cide won the Kentucky Derby with a time of \(2: 01.19,\) or two minutes and 1.19 seconds. The record time for the Kentucky Derby is still held by Secretariat, who won the race with a time of 1: 59.40 in \(1973 .\) How much faster did Secretariat run than Funny Cide 30 years later? (IMAGE CANNOT COPY)

Step-by-Step Solution

Answer

Secretariat ran 1.79 seconds faster than Funny Cide.

Step 1: Convert Times to Seconds

First, we need to convert both Secretariat's and Funny Cide's times to seconds for easier comparison. Funny Cide's time is 2 minutes and 1.19 seconds. We convert this to seconds by calculating: \[ (2 \text{ minutes} \times 60 \text{ seconds/minute}) + 1.19 \text{ seconds} = 120 + 1.19 = 121.19 \text{ seconds} \]Secretariat's time is 1 minute and 59.40 seconds. Converting this to seconds: \[ (1 \text{ minute} \times 60 \text{ seconds/minute}) + 59.40 \text{ seconds} = 60 + 59.40 = 119.40 \text{ seconds} \]

Step 2: Calculate the Time Difference

Now that we have both times in seconds, we subtract Secretatriat's time from Funny Cide's time to find how much faster Secretariat was:\[ 121.19 \text{ seconds} - 119.40 \text{ seconds} = 1.79 \text{ seconds} \]

Key Concepts

Comparison of Times

When you're comparing times, especially in competitions like the Kentucky Derby, it's essential to understand the full contest duration and how it stacks up against historical records or recent performances. In this case, Secretariat and Funny Cide's race times need to be compared directly. However, they are given in a format that mixes minutes and seconds, which can make direct comparison difficult.
One practical approach is to standardize the units you're working with. In most situations, this means converting times entirely into seconds. By doing so, you eliminate the complication of comparing mixed measurement units, such as minutes and seconds, directly.
To perform a fair comparison, always remember:

• Convert all times to the same unit, ideally seconds.
• Ensure accuracy in conversion to maintain precision.

Once everything is converted, subtract the times to see the difference clearly. This reveals how much faster or slower one contestant is relative to another.

Seconds Calculation

Calculating seconds from a given time format is crucial in many time-related problems, especially when precision is key, such as in races and scientific experiments. Converting from a minutes and seconds format to just seconds is straightforward once you get the hang of it.
Let's break down the steps:

• Identify the number of minutes in the original time.
• Remember that 1 minute consists of 60 seconds.
• Multiply the minutes by 60 to convert them to seconds.
• Add any remaining seconds to this total.

For example, Funny Cide's time was 2:01.19. First, convert the 2 minutes into seconds: \[2 \times 60 = 120 \text{ seconds}\]
Then, add the 1.19 seconds: \[120 + 1.19 = 121.19 \text{ seconds}\]
Following this method ensures accuracy and allows meaningful comparison of times.

Time Difference

Finding the difference in times helps to determine performance improvements, historical records, and even personal bests. Once times are converted to a uniform unit, such as seconds, calculating the difference is an easy final step. This is particularly useful in sports where fractions of a second can decide the outcome.
For the two horses, we have both times in seconds:

• Funny Cide: 121.19 seconds
• Secretariat: 119.40 seconds

To find out how much faster Secretariat was, we simply subtract his time from Funny Cide's time: \[121.19 - 119.40 = 1.79 \text{ seconds}\]
This tells us that Secretariat completed the race 1.79 seconds faster than Funny Cide. In events like the Kentucky Derby, this difference is significant and highlights Secretariat's exceptional performance.
Checking calculations carefully ensures that conclusions drawn are accurate, especially in scenarios where precision is paramount.