How Long is 1000 Seconds?

Date: 02/18/2005 at 14:20:51
From: Tiffaney
Subject: Count down from one thousand....

How long does it take to count to one thousand counting one number 
per second?  The detailing of each second, minute, hour, day becomes
confusing to younger children.  

Date: 02/19/2005 at 11:45:35
From: Doctor Wilko
Subject: Re: Count down from one thousand....

Hi Tiffaney,

Thanks for writing to Dr. Math!

Your question: How long does it take to count to one thousand counting 
one number per second?

Answer:  One thousand seconds!  :-)

But probably you want to know how to subdivide 1,000 seconds into 
days, hours, minutes, and seconds.

First, let's just list some facts that we know about time, and then 
we'll come back to the problem.

    60 seconds   =  1 minute

   3,600 seconds =  60 minutes  = 1 hour
   
  86,400 seconds =  1,440 minutes = 24 hours = 1 day

It's often helpful to get a feel for the magnitude of these time 
increments, or even to get an estimate to what our answer should be 
close to before jumping into the calculations.

Just to get a feel for what the answer should be close to, notice 
that it takes 1 hour to count to 3,600 seconds. So you know that to 
count to 1000 seconds it won't even take an hour.  Similarly, it'll 
take 30 minutes to count to 1,800 seconds, and 15 minutes to count to 
900 seconds.

Do you see the power of estimating?  It takes 15 minutes to count to 
900 seconds, so it must take just over 15 minutes to count to 1,000 
seconds!  Now, let's do the math to see the actual answer!

  1,000 seconds       -
  -------------- = 16.6  minutes (or 16 2/3 minutes)
    60 seconds

So far we know that it'll take 16 minutes and some seconds to count 
to 1,000.  How many seconds?  2/3 of a minute.  Let's see what this 
works out to be.

   1 min = 60 sec  (fact)

 2/3 min = (2/3 * 60) sec

 2/3 min = 40 seconds

Final Answer:  To count to 1,000, it'll take 16 minutes and 40 seconds
if you were to count one number per second.

Just to make sure this is right, let's do a check:

  16 minutes = (16 * 60) seconds = 960 seconds 

   960 seconds + 40 seconds = 1,000 seconds  (It checks!)

Once you understand how to do the above problem, then you can have 
some real fun!  How long would it take you to count to one million?  
How old would you be if you were to start counting now and didn't 
stop until you got to one billion?  If you started counting now, 
could you make it to one trillion in your lifetime?  

The answers might suprise you!

Does this help?  Please write back if you need anything else.  :-)

- Doctor Wilko, The Math Forum
  http://mathforum.org/dr.math/