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Numerical Applications

Solve problems on the concept of average speed

Age of a person, hours in a day, duration of a cricket match, etc.– everything represents time. There are two main objects that tell us time: clock and calendar.
Our ancestors used to calculate time by observing the position of the Sun. But that would not be possible during cloudy days and rainy seasons.
In ancient times, people used different types of time-telling instruments like shadow clock, rope clock, water clock, candle clock and sand clock to determine time.

Units of time

Seconds, minutes, hours, days, weeks, months and years are different units of time. We can convert one unit into another by using the relations between them.
Let us learn in detail about the units of time and their relations.

The smallest possible unit of time is second. 60 seconds make 1 minute and 60 minutes make 1 hour.
i.e., 1 minute = 60 seconds and 1 hour = 60 minutes
In other words, 1 second = $\frac{1}{60}$ minutes and 1 minute = $\frac{1}{60}$ hour
Using the above two relations, let us find out the relation between hours and seconds.
We know that 1 hour = 60 minutes
= 60 $\times$ 60 seconds            [$\because$  1 minute = 60 seconds]
= 3600 seconds
$\therefore$ 1 hour = 3600 seconds

There are 24 hours in a day, so we can convert days in terms of minutes or seconds as shown below:
1 day = 24 hours
= 24 $\times$ 60 minutes         [$\because$  1 hour = 60 minutes]
= 1440 minutes
= 1440 $\times$ 60 seconds    [$\because$  1 minute = 60 seconds]
= 86400 seconds
i.e., 1 day = 24 $\times$ 60 minutes = 24 $\times$ 60 $\times$ 60 seconds

So, we have the following:
 1 minute = 60 seconds 1 second = $\frac{1}{60}$ minutes 1 hour = 60 minutes = 3600 seconds 1 minute = $\frac{1}{60}$ hour 1 second = $\frac{1}{3600}$ hour 1 day = 24 $\times$ 60 minutes = 24 $\times$ 60 $\times$ 60 seconds

Now, using the given relations, let us try to convert 18 minutes into seconds.
We know that 1 minute = 60 seconds
In order to convert 18 minutes into seconds, we need to multiply 18 by 60.
$\therefore$ 18 minutes = 18 $\times$ 60 minutes
= 1080 minutes

Now, let us convert 780 minutes into hours.
We know that 1 minute = $\frac{1}{60}$ hour
In order to convert 780 minutes into hours, let us multiply 780 by $\frac{1}{60}$.
$\therefore$ 780 minutes = 780 $\times$ $\frac{1}{60}$ hours
= $\frac{780}{60}$ hours
= 13 hours

24 hour clock
We usually denote time from 12 mid-night to 12 noon as A.M. (Latin: Ante meridiem) and the time from 12 noon to 12 mid-night as P.M. (Latin: Post meridiem).
Look at the following times:
14:40 hours and 20:00 hours
Such representation of times is shown by a 24 hour clock.
In a 24 hour clock, 12 A.M. is represented as 00:00 hours and 12 P.M. is represented as 12:00 hours.
The given tables shows the different formats of time (in A.M.) represented by a 12 hour clock and a 24 hour clock:
 12 hour format 24 hour format 12 A.M. 00:00 hours 1 A.M. 01:00 hours 2 A.M. 02:00 hours 3 A.M. 03:00 hours 4 A.M. 04:00 hours 5 A.M. 05:00 hours 6 A.M. 06:00 hours 7 A.M. 07:00 hours 8 A.M. 08:00 hours 9 A.M. 09:00 hours 10 A.M. 10:00 hours 11 A.M. 11:00 hours

Now, the given table shows the different formats of time (in P.M.) represented by a 12 hour clock and a 24 hour clock:

 12 hour format 24 hour format 12 P.M. 12:00 hours 1 P.M. 13:00 hours 2 P.M. 14:00 hours 3 P.M. 15:00 hours 4 P.M. 16:00 hours 5 P.M. 17:00 hours 6 P.M. 18:00 hours 7 P.M. 19:00 hours 8 P.M. 20:00 hours 9 P.M. 21:00 hours 10 P.M. 22:00 hours 11 P.M. 23:00 hours

It can be observed that from 1 P.M. to 11 P.M., the 24 hour time corresponding to the 12 hour time can be obtained by adding 12 to the hours column.
Conversely, 12 hour time corresponding to 24 hour time for these times can be obtained by subtracting 12 from the hours column.

Railway time
Observe the following table:
 S.no Train Number Name of the Train Place of Departure Destination Departure Time Arrival Time 1. 16235 Mysore Express Tuticorin Madurai Junction 16:35 19:45 2. 12695 Trivandrum Express Chennai Central Salem Junction 15:25 20:10 3. 16860 Maq Chennai Express Coimbatore Junction Tiruchirapalli 15:50 21:50 4. 17229 Sabari Express Coimbatore Junction Salem Juncti…

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