Problem 38 - Elementary Algebra

Question

Find the number of motor vehicle crashes that occur each day. Every 12 minutes someone dies in a motor vehicle crash, every 10 seconds an injury occurs and every 5 seconds a crash occurs. (Source: www.osha.gov, 2005)

Step-by-Step Solution

Answer

17280 crashes per day.

Step 1: Convert time to seconds

First, convert the given time intervals into seconds.1 minute = 60 secondsSo, 12 minutes = 12 * 60 = 720 seconds.Therefore, a fatal crash occurs every 720 seconds.Injury occurs every 10 seconds.A crash occurs every 5 seconds.

Step 2: Calculate the number of seconds in a day

There are 24 hours in a day.1 hour = 3600 seconds.Therefore, the total number of seconds in a day is: 24 * 3600 = 86400 seconds.

Step 3: Calculate the number of crashes per day

To find the number of crashes per day, divide the total number of seconds in a day by the number of seconds between each crash.Number of crashes per day = 86400 seconds / 5 seconds per crash = 17280 crashes per day.

Key Concepts

Understanding Time Conversion

Time conversion helps us change one unit of time into another, like hours to minutes or minutes to seconds. This skill is essential for many mathematical problems, especially those involving rates and frequencies. For example, in our exercise, we converted given time intervals (minutes and seconds) to seconds to simplify calculations. Understanding this process is key to solving problems involving time-based events efficiently.
For instance, to convert hours to minutes, multiply the number of hours by 60 (since 1 hour = 60 minutes). Converting these minutes to seconds involves multiplying by 60 again (1 minute = 60 seconds). Hence, 1 hour is 3600 seconds because 1 hour = 60 minutes and 1 minute = 60 seconds, thus 60 * 60. Practice converting between hours, minutes, and seconds frequently to build confidence in time conversions.

Minute to Seconds Conversion

In our given problem, we needed to convert 12 minutes to seconds to find out how often fatal crashes happen. This process is simple: just multiply the number of minutes by 60 because there are 60 seconds in every minute.

So, for 12 minutes, the calculation is:
\(12 \times 60 = 720 \) seconds.
This conversion makes it easier to compare different rates occurring in seconds, like crashes and injuries. More examples include:

• 5 minutes = \(5 \times 60 = 300\) seconds
• 20 minutes = \(20 \times 60 = 1200\) seconds

These conversions simplify complex time-based calculations, especially when combined with other measurements.

Calculating Rates

Calculating rates involves determining how often an event happens within a particular unit of time. In our problem, we calculated the rate of motor vehicle crashes. Here's the breakdown:
1. We first converted all given times to seconds.
2. We calculated the total number of seconds in a day.
3. We then used these conversions to find the number of incidents occurring per day.
For example, knowing a crash occurs every 5 seconds:
Total seconds in a day = \(24 \times 3600 = 86400\)
Then, divide by the time interval:
\(86400 \, \text{seconds/day} \div 5 \, \text{seconds/crash} = 17280 \, \text{crashes/day}\)
This method is useful in various scenarios such as determining the number of heartbeats per minute if you know the rate per second or figuring out the number of pedestrians passing a point each hour if you have their frequency per minute. Understanding and practicing this concept helps handle diverse real-life calculations more comfortably.