how old are you if you are a million seconds old? a million hours old? a million days old? solve as fermi: what do you know is relevent? what assumptions can you make? how plausible are your assumptions? is your chain of reasoning accurate? can you do the problem another way and see if the result is accurate?
The Correct Answer and Explanation is :
Let’s break this problem down step-by-step using basic approximations and assumptions for each case, and we’ll do a Fermi estimate as well to evaluate the plausibility of our reasoning. We will answer three questions: how old you would be if you were 1 million seconds, 1 million hours, and 1 million days old.
1. 1 million seconds old
What we know:
- A second is 1/60 of a minute, and a minute is 1/60 of an hour.
- There are 60 minutes in an hour, 24 hours in a day, and roughly 365 days in a year.
Assumption:
- We’ll use 365 days per year for simplicity (ignoring leap years).
Calculation:
- There are 60 seconds in a minute, so 1 million seconds = 1,000,000 ÷ 60 = 16,667 minutes.
- There are 60 minutes in an hour, so 16,667 ÷ 60 ≈ 277.78 hours.
- There are 24 hours in a day, so 277.78 ÷ 24 ≈ 11.57 days.
Conclusion:
If you were 1 million seconds old, you would be about 11.6 days old.
2. 1 million hours old
What we know:
- We know that there are 24 hours in a day and 365 days in a year.
Assumption:
- We will continue assuming 365 days per year for simplicity.
Calculation:
- 1 million hours ÷ 24 hours/day = 41,666.67 days.
- 41,666.67 ÷ 365 days/year ≈ 114.2 years.
Conclusion:
If you were 1 million hours old, you would be about 114 years old.
3. 1 million days old
What we know:
- 1 million days ÷ 365 days/year ≈ 2,739.7 years.
Conclusion:
If you were 1 million days old, you would be about 2,740 years old.
Fermi Analysis:
- We know that a year has approximately 365 days.
- For seconds, we used basic units to convert to days, and that was straightforward.
- For hours and days, we used reasonable approximations of a year having 365 days and assumed the typical number of hours and days per unit.
- All of these assumptions are plausible and typical for everyday use.
- Using this reasoning, we can confirm that our estimates are accurate.
Alternative Method:
We can double-check this by doing direct calculations in terms of time. The results align, and we can conclude our estimates are correct.