A Billion Seconds

Date: 10/21/96 at 12:47:59
From: Anonymous
Subject: When a Billion Seconds

If I was born on 01/02/84, on what day and what year, month will I 
have been alive for a billion seconds?

Date: 10/22/96 at 10:52:8
From: Doctor Ken
Subject: Re: When a Billion Seconds

Hi Alvina -

To solve this kind of problem, you need to first figure out how many 
seconds there are in an hour, in a day, in a week, in a year, and so 
on.  To really do this problem right, you'd have to take into account 
leap years (which can get pretty complicated - they don't just happen 
every 4 years; there are some other rules that they follow) and leap 
seconds (yup - they happen!).  

But in this solution, I'm not going to take these factors into 
account, so that you can see the general strategy behind how you'd 
solve this problem.

Okay, here we go!  There are 60 seconds in a minute, and 60 minutes 
in an hour.  So there are 60 x 60 seconds in an hour, in other words 
3600 seconds in an hour.  Furthermore, there are 24 hours in a day, 
so there are 24 x 3600 seconds = 86400 seconds in a day.  Also, there 
are 365 days in a year, so there are 365 x 86400 seconds = 31,536,000 
seconds in a year.  Let's summarize this in a table:

1 hour = 3600 seconds
1 day  = 86400 seconds
1 year = 31,536,000 seconds

So how many years does it take to reach 1,000,000,000 seconds?  Well, 
31 x 31,536,000 =   977,616,000 and
32 x 31,536,000 = 1,009,152,000.  

So 31 years is not enough, and 32 years is too much.  Looks like it's 
going to be 31 years plus a little bit.  

How much?  Well, 1,000,000,000 - 977,616,000 = 22,384,000.  So we need 
to figure out how many months and days that is.  I'll leave this part 
of the problem for you to figure out - it can be a little tricky to 
figure out how many seconds are in each month, but you can use the 
figure we found above, the number of seconds in a day, to figure this 
out.  Good luck!

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/