Subtracting Time Expressions

Date: 10/09/2005 at 13:52:17
From: madison
Subject: subtracting years,days,hours,minutes and seconds

How do I subtract two amounts of time, like

  5 years, 21 days, 4 hours, 32 minutes, 17 seconds
- 2 years, 93 days, 7 hours, 47 minutes, 24 seconds 

How would you subtract all the numbers together?

Date: 10/09/2005 at 14:18:08
From: Doctor Ian
Subject: Re: subtracting years,days,hours,minutes and seconds


Hi Madison,

Think about how we would do a subtraction like

   214
  - 86   
  ----

We could write this as

    200  10   4
  -   0  80   6
  -------------

then we have to exchange items from larger groups for items in smaller
groups.  For example, we could exchange 1 group of 100 for 10 groups
of 10:

    100  110   4
  -   0   80   6
  --------------

And then we could exchange 1 group of 10 for 10 groups of 1:

    100  100  14
  -   0   80   6
  --------------

And now we can just do the individual subtractions:

    100  100  14
  -   0   80   6
  --------------
    100   20   8  = 128

Does that make sense?  Dealing with time is the same idea, but the
group sizes aren't 10's.  There are 365 days in a year, so

    5 years, 21 days, 4 hours, 32 minutes, 17 seconds
  - 2 years, 93 days, 7 hours, 47 minutes, 24 seconds 
  ---------------------------------------------------

becomes

    4 years, 386 days, 4 hours, 32 minutes, 17 seconds
  - 2 years,  93 days, 7 hours, 47 minutes, 24 seconds 
  ----------------------------------------------------

There are 24 hours in a day, so that becomes

    4 years, 385 days, 28 hours, 32 minutes, 17 seconds
  - 2 years,  93 days,  7 hours, 47 minutes, 24 seconds 
  -----------------------------------------------------

There are 60 minutes in an hour, so that becomes

    4 years, 385 days, 27 hours, 92 minutes, 17 seconds
  - 2 years,  93 days,  7 hours, 47 minutes, 24 seconds 
  -----------------------------------------------------

And there are 60 seconds in a minute, so that becomes

    4 years, 385 days, 27 hours, 91 minutes, 77 seconds
  - 2 years,  93 days,  7 hours, 47 minutes, 24 seconds 
  -----------------------------------------------------

And now you can just do the individual subtractions.

Does this make sense? 

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