**Elapsed Time**

*How long did it take? How much time passed?*

The answer to these types of questions is answered by finding the elapsed time.

Let's start with a definition:

elapsed time: the difference between the final time and the initial time.

To find out how much time passes, we can subtract the clock or stopwatch reading at the beginning of the event from the clock or stopwatch reading at the end. With that in mind,

initial time is the clock or stopwatch reading at the beginning of an event. For a stopwatch, it could often be zero.final time is the clock or stopwatch reading at the end of an event.

For example, a track coach starts a stopwatch when the gun fires and stops it when the runner crosses the finish line. The initial time reading was zero and the final reading on the stopwatch was 10.5 seconds. Thus, the time that the runner ran was 10.5 seconds.

Elapsed time will always be expressed with time units, such as seconds, minutes, hours, etc.

Calculating elapsed time is generally easy to understand. If your movie starts at 7:00 and ends at 9:15, how long does it last? Or, in other words:

What is the elapsed time of a movie that begins at 7:00 and ends at 9:15?

Most people will almost instantly say 2 hours and 15 minutes. But wait! There is actually a math way to do this with math!

If elapsed time is t and initial time is ti and final time is tf, then:

*t = tf - ti*

Of course, having a formula spoils the simplicity of the concept, but it also allows for the concept to be applied in non-intuitive situations. But, for now, the example above:

*t =*what we are looking for

*tf = 9:15 o'clock*

*ti =*7:00 o'clock

*9:15*

*- 7:00*

*______*

*2:15 hours*

The process becomes more complex when you have to "borrow"

*because, time.*A minute is 60 seconds. An hour is 60 minutes. So when you borrow, you have to borrow 60 of the other thing.
Thus, the problem goes like this:

*t =*what we are looking for

*tf = 9:15 o'clock*

*ti =*7:30 o'clock

*9:15*

*- 7:30*

*______*

*????*

When you borrow 60 minutes so that you can subtract, you get this:

*8:75*

*- 7:30*

*______*

This can be extended to days, as well, though with less clarity.

*(What do you mean by "day"? Is it 24 hours or is it the actual amount of time that it takes for the earth to rotate once, which is more than 24 hours?)*
When reading a stopwatch, you will see the readings written like this:

HH:MM:SS.fs

Where HH is hours, MM is minutes, SS is seconds and fs is fractions of a second.

The math works the same—if you borrow, you have to borrow in 60s.

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