Time
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24 Hour Clock
   
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No doubt you will already have seen the 24-hour clock in use on railway timetables, for example (Other countries make much more use of it than in Britain).
The '12 hour' clock requires that times are followed by either 'a.m.' or 'p.m' in order to avoid ambiguity.
Times on the 24 hour clock are always represented by four numbers - but nothing else is required to be added.
- Some people just write four numbers, e.g. 0452, 0930, others insert a colon in the middle, e.g. 04:52, 09:30.
- Times like 0900, 1300 are commonly stated as 9 hundred hours or 13 hundred hours
- Midnight on the 24 hour clock is either 2400 or 0000, but times in the first hour after midnight will always be of the form 0049, 0001, etc. Having said that, note that 0000 is often the only notation used for midnight on things like Internet booking sites where it is essential to remove any ambiguity
Decimal Form
Note that
7 hrs 30 mins = 7.5 hrs
It is definitely NOT 7.3 hours.
Converting time to a decimal form is necessary if the time is to be used in arithmetic calculations.
Example
If 720 items are produced in a factory in 7 hours 30 mins, how many are produced per hour on average
720 / 7.5
= 96
You definitely do not state the denominator as 7.3 hours, this would give you the wrong answer. The correct denominator is 7.5 hours.
To express minutes as a decimal (of an hour) you might find it easier to first convert to a fraction, and then convert this fraction to a decimal, e.g. to express 12 mins as a decimal (of an hour)
- First state as a fraction of an hour
12 / 60 - Convert to a decimal by treating this fraction as a division
0.2
With experience, you can introduce shortcuts, e.g. you could recognize the fact that 6 mins is 0.1 hours, so
You might like to view this
conversion chart
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Time Intervals
In everyday life, time is not usually represented in a decimal form, so we need to use a slightly different technique to find the interval between two specific times.
Example
To find the time between 0320 and 0945, the technique would be :
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So the calculation is :
= 5 hours + 1 hour + 25 minutes
= 6 hours + 25 minutes
Alternatively you could just say :- from 0320 to 0920 is 6 hours and from 0920 to 0945 is another 25 minutes, therefore the total time interval is 6 hours and 25 minutes
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Average Speed
Average Speed = Distance Travelled ÷ Time Taken
From which we can derive
I have used simple algebra to derive the last two equations, but you could derive these formulae separately, without algebra, by just thinking about the physical situation. If you are not too happy with algebra, just spend a bit of time convincing yourself that the last two formulae are correct, and think how you would be able to produce them to solve a given question ( by that, I mean if you can understand the logic, you should be able to reproduce them without necessarily committing the formulae to memory).
Example : If a car covers 720 km in 7 hours 30 mins, what is its average velocity ?
= 750 / ( 7 hrs 30 mins )
= 750 / 7.5 = 100 km / hr
Example : If a train travels for 3 hours at an average speed of 35 km/hr, how far has it traveled ?
= 35 × 3
= 105 kms
Example : If a journey involves a distance of 3000 kilometres hours at an average speed of 35 km/hr, how long will the journey take ?
= 3000 ÷ 35
= 85.71 hours (to 2 d.p.)
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Average Speed - Part 2
A more complicated example
A car travels 60 km at 30 km/hr, and then a further 120 km at an average
speed of 40 km/hr. Work out its average speed for the entire journey.
Given that the formula is
Average Speed for Entire Journey = Total Distance Travelled ÷ Total Time Taken
A car travels 60 km at 30 km/hr, and then a further 120 km at an average speed of 40 km/hr. Work out its average speed for the entire journey.
We need to know the
What we don't know yet is the total time taken, which is more complicated.
So consider each stage separately.
So the Total Time Taken = 2 + 3 = 5 hours.
So finally the average speed is given by
= 180 / 5 = 36 km / hr