By studying this lesson, you will be able to,
● Identify the units of measuring time,
● Identify the relationships between different units of measuring time,
● Find the time taken for an activity,
● Express the time in terms of the 24 hour clock and
● Write the date in tandard form.
Find a clock similar to the one shown in the figure, which shows the correct time and observe it carefully.
● In this clock, the circular edge has been divided into 60 equal parts by short line segments.
●The numbers from 1 up to 12 have been marked on the face of the clock, such that there are five equal parts between any two adjacent numbers.
● From the three hands which are fixed at the centre, the shortest hand is the hour hand. The narrow hand in red is the seconds hand, and the remaining hand is the minute hand.
● The three hands rotate in the direction in which the numbers on the face are increasing.
● The time it takes for the pointed end of the hour hand to move from one number to the next is one hour.
● The time it takes for the pointed end of the minute hand to move from one short line segment to the next is one minute.
● The time it takes for the pointed end of the seconds hand to move from one short line segment to the next is one second.
● During an hour, the minute hand rotates one round.
1 hour = 60 minutes
● During one minute the seconds hand rotates one round.
1 minute = 60 seconds
● When the time is being read, the hour is taken to be the number which the hour hand is pointing towards or has last passed.
● The number of minutes and the number of seconds is taken to be the number of line segments each hand has last passed or is pointing towards.
Let us read the time denoted by the clock in the figure.
Since the hour hand lies between the numbers 10 and 11,
the number that the hour hand has last passed is 10.
The minute hand lies between the 25th and 26th line segments. Hence, the line segment that the minute hand has last passed is 25. The seconds hand is pointing towards the 13th line segment.
Therefore, the time is read as 25 minutes and 13 seconds past 10. This is written as 10.25.13. Sometimes, the number of seconds is not indicated. In such a case, the time is expressed as 10.25.
Exercise 4.1
(1) Write down the time denoted by each of the following clock faces,in terms of hours, minutes and seconds.
● Identifying the periods a.m. (ante meridiem) and p.m. (post meridiem)
The time according to both the above clocks is 7.00.
One clock shows the time a child goes to school as 7.00 in the morning.
The other clock shows the time a child is studying as 7.00 in the evening.
Accordingly, since the clock shows the same time at two different instances of the day, how the time is indicated precisely is described below.
When all three hands of a clock point at 12 during the day time, the time is 12 noon.
When all three hands of a clock point at 12 during the night time, the time is 12 midnight.
The 12 hour time period between 12 midnight and 12 noon is known as “ante meridiem” (before midday).
The 12 hour time period between 12 noon and 12 midnight is know as “post meridiem” (after midday).
The period of time from 12 midnight of one day to 12 midnight of the next is called a day.
The hour hand completes two rounds of the clock during a day.
That is, one day = 2 periods = 24 hours
Accordingly, in the above example,
7.00 in the morning is denoted by 7.00 a.m. (ante meridiem is written in short as a.m.)
7.00 in the evening is denoted by 7.00 p.m. (post meridiem is written in short as p.m.)
4.2 Reading the time on a 24 hour clock
The figure depicts a 24 hours clck. The numbers from 1 to 12 have been marked around the outer edge, and the numbers 13 up to 24 have been marked on an inner circle.
The ante meridiem time is read by considering the numbers from 1 to 12 and the post meridiem time is read by considering the number from 13 upto 24. The day starts at midnight. This time is denoted by 00:00. Also, the day ends at midnight.This time is denoted by 24 :00.
The time, 30 minutes past the starting time of the day is denoted as 00:30.
10.30 a.m. is expressed as 10:30.
12 noon is expressed as 12:00.
1.00 p.m. is expressed as 13:00.
6.00 p.m. is expressed as 18:00.
The time is written in international standard form as follows.
Hours : Minutes : Seconds
hh : mm : ss
In this form, the hours, minutes and seconds have all to be expressed using two digits. When the number of seconds is not required, the time is expressed in hours and minutes.
For example, 3 minutes and 48 seconds past 1 in the afternoon written in international standard form is 13:03:48.
The following table shows how different times within the same day are written in international standard form
Example 1
Write 2.35 p.m. in international standard form. The answer is 14 :35.
Exercise 4.2
(1) The following table provides information on the time of departure of several flights, flying out from the Bandaranaike International Airport. Copy the table and fill in the blanks.
(2) Re-write the following sentences expressing the given time in international standard form.
(i) The train “Udarata Menike” which leaves the Fort station at
10.30 a.m. is expected to reach Badulla at 5.40 p.m.
(ii) The prize giving, which commences at 11.00 a.m. is expected
to conclude at 2.30 p.m.
(iii) The mathematics test, which commences at 11.30 a.m. will
end at 1.30 p.m.
(3) Express the times given in the following table in terms of the 12 hour clock .
4.3 Representing the date in standard form
When writing the date in standard form,
● first the year, then the month and finally the day should be written.
● four digits should be used to represent the year, two digits to represent the month and two digits to represent the day.
The 8th of April, 2015 is represented in international standard form as 2015 - 04 - 08.
The time the day 2015 - 05 - 08 ends at 12 midnight is represented by 2015 - 05 - 08 24:00. This time can also be written as 2015 - 05 - 09 00:00.
4.4 Relationships between units of measuring time
Seconds, minutes, hours and days are several units that are used to measure time. Now, let us consider the relationships between these units.
● Representing time given in minutes, in terms of seconds
Since
1 minute = 60 seconds,
2 minutes = 120 seconds and
3 minutes = 180 seconds.
That is, to represent the time given in minutes, in terms of seconds, the given number of minutes needs to be multiplied by 60.
Example 1
Express 8 minutes in seconds.
1 minute = 60 seconds
8 minutes = 60 × 8 seconds
= 480 seconds
Exercise 4.3
(1) Express each of the following times given in minutes, in terms of seconds.
(i) 1 minute
(ii) 6 minutes
(iii) 30 minutes
(iv) 20 minutes
(v) 38 minutes
(vi) 48 minutes
2 Representing time given in seconds, in terms of minutes
Since
60 seconds = 1 minute,
120 seconds = 2 minutes and
180 seconds = 3 minutes.
That is, to represent time given in seconds, in terms of minutes, the given number of seconds needs to be divided by 60.
Exercise 4.4
(1) Express each of the following times given in seconds, in terms of minutes.
(i) 60 seconds
(ii) 120 seconds
(iii) 240 seconds
(iv) 300 seconds
(v) 1200 seconds
(vi) 3600 seconds
(2) Express each of the following times given in seconds, in terms of minutes and seconds.
(i) 75 seconds
(ii) 100 seconds
(iii) 150 seconds
(iv) 200 seconds
(v) 250 seconds
(vi) 325 seconds
2 Representing time given in hours, in terms of minutes
Since
1 hour = 60 minutes,
2 hours = 120 minutes and
3 hours = 180 minutes.
That is, to represent time given in hours, in terms of minutes, the given number of hours needs to be multiplied by 60.
Exercise 4.5
(1) The conversions done to find the number of seconds in one hour are given below. Write down the numbers suitable for the blank boxes.
1 hour = 🔲 minutes = 🔲 seconds
(2) Express each of the following times given in hours, in terms of minutes.
(i) 1 hour
(ii) 2 hours
(iii) 3 hours
(iv) 5 hours
(v) 12 hours
(vi) 24 hours
2 Representing time given in minutes, in terms of hours
Since
60 minutes = 1 hour,
120 minutes = 2 hours and
180 minutes = 3 hours.
That is, to represent time given in minutes, in terms of hours, the given number of minutes needs to be divided by 60.
Exercise 4.6
(1) Express each of the following times given in minutes, in terms of hours.
(i) 60 minutes
(ii) 180 minutes
(iii) 540 minutes
(iv) 300 minutes
(v) 360 minutes
(vi) 600 minutes
(2) Express each of the following times given in minutes, in terms of hours and minutes.
(i) 90 minutes
(ii) 100 minutes
(iii) 115 minutes
(iv) 150 minutes
(v) 245 minutes
(vi) 320 minutes
2 Relationship between days and hours
Since
1 day = 24 hours,
2 days = 48 hours and
3 days = 72 hours.
That is, to represent a certain number of days in hours, the given number of days needs to be multiplied by 24.
Similarly,
24 hours = 1 day
48 hours = 2 days
72 hours = 3 days
That is, to represent a time given in hours, in terms of days, the given number of hours needs to be divided by 24.
Exercise 4.7
(1) Express each of the following times in hours.
(i) 1 day
(ii) 2 days
(iii) 3 days
(iv) 5 days
(v) 8 days
(vi) 30 days
(2) Express the following times in days.
(i) 24 hours
(ii) 48 hours
(iii) 96 hours
(iv) 120 hours
(v) 240 hours
(vi) 360 hours
(3) Express the following times in days and hours.
(i) 34 hours
(ii) 58 hours
(iii) 80 hours
(iv) 130 hours
(v) 255 hours
(vi) 400 hours
(4) The conversion steps carried out by a certain student to obtain the number of seconds in a day is given below,
Find the number suitable for each box.
(5) Join the pairs that express the same time.
Now, let us find the elapsed time by considering two times.
Sumith’s mother left home at 2.00 p.m. to visit the market. She returned home at 3.30 p.m. Let us find the time that has elapsed from the moment she left her home until she returned from the market.
Method 1
The time period between 2.00 p.m. and 3.00 p.m. is 1 hour. The time period between 3.00 p.m. and 3.30 p.m. is 30 minutes. Therefore, the time that has elapsed is 1 hour and 30 minutes.
● Elapsed time corresponding to an incident which has occured during a period (a.m. or p.m.) can be found easily as follows.
Method 2
Time his mother returned home = 3.30 p.m.
Time his mother left home = 2.00 p.m.
To find the time that has elapsed, the difference between the time she returned and the time she left has to be found.
To find the time that has elapsed, the difference between the time she returned and the time she left has to be found.
Accordingly, the time that elapsed between the time Sumith’s mother left home and the time she returned is 1 hour and 30 minutes.
To find the elapsed time of a task or an event, the difference between the time it started and the time it ended needs to be found.
Example 1
To prepare for the term test, Samith’s sister studied from 7.30 p.m. to10.15 p.m. yesterday. Find the time his sister spent studying.
Time she finished studying = 10.15 p.m.
Time she started studying = 7.30 p.m.
Here both the times are in p.m.
To find the time she spent studying, let us find the difference between the time she started studying and the time she finished studying.
● Since 30 minutes cannot be subtracted from 15 minutes, let us carry 1 hour, that is 60 minutes, from the 10 hours in the hours column to the minutes column.
● Then, number of minutes = 15 + 60 minutes = 75 minutes.
● Now, let us subtract 30 minutes from 75 minutes. Then we obtain 45 minutes.
● Now, let us subtract 7 hours from the remaining 9 hours in the hours column. Then we obtain 2 hours.
● Therefore, the answer is 2 hours and 45 minutes.
Example 2
A school prize giving started at 9.30 a.m. and ended at 1.45 p.m. Find the duration of the event. Since the starting time is ante meridiem and the ending time is post meridiem, to find the duration, let us write the time according to the 24 - hour clock.
Starting time = 09:30
Ending time = 13:45
Duration = 13:45 – 09:30
= 4 hours and 15 minutes
In problems related to elapsed time (or duration), corresponding to incidents which have occurred during the same day, it is convenient to solve the problem by writing the time, according to the 24 - hour clock.
Exercise 4.8
(1) The way Sameera spent his time from 3.00 p.m. to 7.00 p.m. is given below. The clocks indicate the starting time and ending time of each activity he was involved in. Find the time in minutes that he spent on each activity by considering the times indicated by the clocks.
(2) Copy the following table and complete it.
(3) There are two routes from Kurunegala to Anuradhapura.
(i) A bus which left Kurunegala at 5.10 a.m. reached Anuradhapura at 7.55 a.m. passing through Ambanpola. Find the time this journey took.
(ii) A bus which left Kurunegala at 5.45 a.m. reached Anuradhapura at 8.20 a.m. passing through Dambulla. Find the time this journey took.
(iii) Via which of the above routes will a person reach Anuradhapura in less time?
(4) The agenda of a prize giving is given below.
8.30 a.m. – Guests enter the hall in a procession accompanied
by a perahera.
8.40 a.m. – Lighting of the traditional oil lamp
8.45 a.m. – Welcome song
8.50 a.m. – Welcome speech (Principal)
9.05 a.m. – Prize distribution - Primary section
9.35 a.m. – Chief Guest’s speech
9.50 a.m. – Prize distribution - Secondary section
10.25 a.m. – Drama
10.45 a.m. – Prize Distribution - To those selected to the
university
11.00 a.m. – Vote of Thanks
11.10 a.m. – National Anthem and the end of the event
Find the time allocated for each of the following.
(i) Welcome speech
(ii) Chief Guest’s speech
(iii) Prize distribution - Primary section
(iv) Drama
(v) Prize distribution - Secondary section
4.6 Addition of time described further
A bus takes 1 hour and 30 minutes to travel from Matara to Galle and 3 hours and 20 minutes to travel from Galle to Colombo. Let us find the total time it takes for the bus to travel from Matara to Colombo.
Time taken to travel from Matara to Galle = 1 hour and 30 minutes
Time taken to travel from Galle to Colombo = 3 hours and 20 minutes
Let us add these two times to find the total time taken for the journey.
Let us add the minutes in the minutes column.
50 minutes + 40 minutes = 90 minutes
90 minutes = 1 hour and 30 minutes
Let us write the 30 minutes in the minutes column. Let us carry the 1 hour to the hours column and add the hours in that column. 1 + 3 + 4 = 8. That is, 8 hours
The answer is 8 hours and 30 minutes.
Let us add the seconds in the seconds column.
45 seconds + 30 seconds = 75 seconds
75 seconds = 60 seconds + 15 seconds
Since, 60 seconds = 1 minute,
75 seconds = 1 minute + 15 seconds
Let us write the 15 seconds in the seconds column.
Let us carry the 1 minute to the minutes column and
add the minutes in that column.
1 + 3 + 5 = 9. That is, 9 minutes.
The answer is 9 minutes and 15 seconds.
Example 5
Let us add the hours in the hours column.
20 hours + 15 hours = 35 hours
35 hours = 24 hours + 11 hours
Since 24 hours = 1 day,
35 hours = 1 day + 11 hours
Let us write the 11 hours in the hours column.
Let us carry the 1 day to the days column and add the days in that column.
1 + 2 + 3 = 6. That is, 6 days.
The answer is 6 days and 11 hours.
Exercise 4.9
(13) The timings of 4 athletes who participated in a 4 × 400 metres relay are given below.
Find the total time taken by the four athletes to complete the relay.
If the Mathematics I paper starts at 8.00 a.m., at what time does the Mathematics II paper end?
(15) A man travelled a part of a journey by bus. The bus journey lasted1 hour and 45 minutes. He walked the remaining part of the journey in 35 minutes. Find the total time the man spent on this journey.
(5) 12 minutes and 40 seconds have been allocated for advertisements to be run during a TV programme which is telecasted from 7.00 p.m. to 7.30 p.m.. During this period, for how much time is the programme shown?
