Question

If you could say hello to a new person every second without taking a break and working around the clock, how many years would it take you to greet the 85 million people who were added to the world's population in 2013? (Hint: start by dividing 85 million seconds by 60 to find the number of minutes, and go from there to find the number of years.) How many years would it take for you to greet 7.1 billion people?

Short answer

It takes about 2.7 years to greet 85 million people and 225 years to greet 7.1 billion people.

Step-by-step solution

Calculate Minutes

To find how many minutes it takes to greet 85 million people, divide the total seconds by 60. \[ \text{Minutes} = \frac{85,000,000}{60} \]

Calculate Hours

To convert the number of minutes into hours, divide the number of minutes by 60.\[ \text{Hours} = \frac{1,416,666.67}{60} \approx 23,611.11 \]

Calculate Days

Now, convert hours to days by dividing by 24 since there are 24 hours in a day.\[ \text{Days} = \frac{23,611.11}{24} \approx 984 \]

Calculate Years

Finally, convert days into years by dividing by 365 (assuming no leap years for simplicity).\[ \text{Years} = \frac{984}{365} \approx 2.7 \]

Repeat Steps for 7.1 Billion

Now redo the calculations for 7.1 billion people.1. Convert seconds to minutes: \[ \text{Minutes} = \frac{7,100,000,000}{60} \] 2. Convert minutes to hours: \[ \text{Hours} = \frac{118,333,333.33}{60} \approx 1,972,222.22 \] 3. Convert hours to days: \[ \text{Days} = \frac{1,972,222.22}{24} \approx 82,175.93 \] 4. Convert days to years: \[ \text{Years} = \frac{82,175.93}{365} \approx 225 \]

Conclusion

To greet 85 million people, it takes approximately 2.7 years. To greet 7.1 billion people, it takes approximately 225 years.

Key concepts

Mathematical Modeling

Mathematical modeling is a technique used to simplify complex real-world problems by using mathematical expressions to represent these problems. Through mathematical equations and logic, we can make calculations, predictions, or decisions. In this case, the scenario involves computing how long it would take to greet each person who was added to the world population in 2013 and the entire global population if you greeted one person per second.

The essence of modeling here is to break down the greeting process into manageable parts: seconds, minutes, hours, days, and finally years. By using simple arithmetic operations like division, we convert these units sequentially. This systematic breakdown allows us to understand how vast numbers, such as 85 million or 7.1 billion, translate into time, giving us a practical perspective on these large figures.

It's crucial to note how these steps abstract a complex problem into a series of straightforward actions. Mathematical modeling thus provides a framework to make sense of the data and inform us of real-world issues like population growth without overwhelming us with their raw magnitude.

World Population

The world population is a vast and dynamic entity that reflects the number of people living on our planet. As of 2013, an additional 85 million people were added to the global count, showcasing how quickly the world population can grow. Understanding population growth involves recognizing factors such as birth rates, death rates, and migration, which all contribute to these numbers.

The exercise of greeting each new person within one second may sound simple, yet it starkly demonstrates the rapid increase in global population. With 7.1 billion people residing worldwide around that time, imagining greeting each individual brings awareness to the vastness and diversity of humanity.

Managing and understanding population growth is essential, as it affects resources, economics, and society as a whole. By contextualizing numbers and percentages involved in global population studies, we form a better understanding of their real-world implications and the challenges posed by sustaining such large numbers of people on our planet.

Time Conversion

Time conversion simplifies the process of changing one time unit to another, allowing us to comprehend durations in more meaningful ways. In our exercise, the starting point is seconds, which are converted into minutes, hours, days, and finally years. This cascading conversion helps in visualizing how much time it takes for activities we often overlook on a daily basis.

- **Seconds to Minutes:** We begin by dividing the number of seconds by 60, as there are 60 seconds in a minute. This provides a baseline for larger units of time.
- **Minutes to Hours:** Similarly, each hour contains 60 minutes, so dividing the total minutes by 60 converts them into hours, expressing time on a higher scale.
- **Hours to Days:** With 24 hours making up a day, dividing the total hours by 24 yields the number of days, aligning time with the human daily cycle.
- **Days to Years:** Finally, understanding time in years is often most relatable, especially for long durations. By dividing by 365, we account for the non-leap year length of a calendar year.
This step-by-step conversion process assists in appreciating duration and scales, enhancing our ability to grasp otherwise abstract timelines. This knowledge is incredibly useful when dealing with significant periods, such as those required to greet millions or billions of people, which reinforce the vastness of both global time and population growth.