Problem 37
Question
Find the number of nonfatal injuries in alcohol-related motor vehicle crashes that occur each day. Alcohol-related motor vehicle crashes kill someone every 31 minutes and nonfatally injure someone every two minutes. (Source: www.cdc.gov)
Step-by-Step Solution
Verified Answer
720 nonfatal injuries per day
1Step 1: Understand the Problem
Determine the frequency of nonfatal injuries from the given data. Nonfatal injuries occur every 2 minutes.
2Step 2: Determine Total Minutes in a Day
Calculate the total number of minutes in a day. Since there are 24 hours in a day and 60 minutes in an hour, the total number of minutes in a day is given by: \[ 24 \times 60 = 1440 \text{ minutes} \text{ per day} \]
3Step 3: Calculate Number of Nonfatal Injuries
Determine the number of nonfatal injuries per day by dividing the total number of minutes in a day by the frequency of nonfatal injuries: \[ \frac{1440 \text{ minutes}}{2 \text{ minutes/injury}} = 720 \text{ nonfatal injuries per day} \]
Key Concepts
Frequency of InjuriesCalculation of MinutesRate of Events
Frequency of Injuries
Alcohol-related motor vehicle crashes result in many tragedies. One important measure to understand the severity of these problems is the frequency of injuries.
The problem states that nonfatal injuries happen every 2 minutes.
This means the interval between one injury and the next is 2 minutes.
Understanding this frequency helps in comprehending the magnitude of the issue. In such cases, frequency lets us calculate broader statistics such as total daily injuries. This makes it easier to grasp the large scale of nonfatal injuries caused by these crashes.
Recognizing the frequency allows for better planning and emergency response, and helps in structuring public awareness campaigns effectively.
Knowing the frequency lays the groundwork for more in-depth calculations, including understanding the rate of events and necessary response efforts.
The problem states that nonfatal injuries happen every 2 minutes.
This means the interval between one injury and the next is 2 minutes.
Understanding this frequency helps in comprehending the magnitude of the issue. In such cases, frequency lets us calculate broader statistics such as total daily injuries. This makes it easier to grasp the large scale of nonfatal injuries caused by these crashes.
Recognizing the frequency allows for better planning and emergency response, and helps in structuring public awareness campaigns effectively.
Knowing the frequency lays the groundwork for more in-depth calculations, including understanding the rate of events and necessary response efforts.
Calculation of Minutes
Before you can determine the number of nonfatal injuries in a day, it's essential to know the total number of minutes in a day.
We start with knowing there are 24 hours in one day.
To convert hours into minutes, simply multiply the number of hours by 60 (since there are 60 minutes in one hour).
So, calculate: \[ 24 \times 60 = 1440 \text{ minutes per day} \]
This conversion is crucial as it provides the base unit (minutes) for further calculations.
Understanding how to convert hours to minutes can be useful in many other situations as well, not just in this specific problem.
Mastering this simple yet fundamental calculation opens the door to more complex problem-solving and allows for confident handling of time-based statistics.
We start with knowing there are 24 hours in one day.
To convert hours into minutes, simply multiply the number of hours by 60 (since there are 60 minutes in one hour).
So, calculate: \[ 24 \times 60 = 1440 \text{ minutes per day} \]
This conversion is crucial as it provides the base unit (minutes) for further calculations.
Understanding how to convert hours to minutes can be useful in many other situations as well, not just in this specific problem.
Mastering this simple yet fundamental calculation opens the door to more complex problem-solving and allows for confident handling of time-based statistics.
Rate of Events
With the total number of minutes in a day known, we can now find the rate at which nonfatal injuries occur.
The frequency of nonfatal injuries is every 2 minutes.
To find out how many injuries happen daily, you need to divide the total minutes in a day by the frequency of injuries.
This calculation is as follows: \[ \frac{1440 \text { minutes}}{2 \text { minutes/injury}} = 720 \text { nonfatal injuries per day} \]
This means there are 720 nonfatal injuries from alcohol-related motor vehicle crashes each day.
Understanding how to calculate rates can be very powerful.
It allows for insight into recurring events over time and is useful in fields such as epidemiology and public health.
Being able to calculate rate of events equips you with a valuable tool for analyzing similar problems, thereby fostering better decision-making and planning.
Such understanding provides a clearer picture and helps in formulating effective interventions.
The frequency of nonfatal injuries is every 2 minutes.
To find out how many injuries happen daily, you need to divide the total minutes in a day by the frequency of injuries.
This calculation is as follows: \[ \frac{1440 \text { minutes}}{2 \text { minutes/injury}} = 720 \text { nonfatal injuries per day} \]
This means there are 720 nonfatal injuries from alcohol-related motor vehicle crashes each day.
Understanding how to calculate rates can be very powerful.
It allows for insight into recurring events over time and is useful in fields such as epidemiology and public health.
Being able to calculate rate of events equips you with a valuable tool for analyzing similar problems, thereby fostering better decision-making and planning.
Such understanding provides a clearer picture and helps in formulating effective interventions.
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