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Time: Seconds, 24-hour Clock and Duration

Seconds

clock showing hour hand, minute hand and second hand

The second is a unit of measurement of time. It is smaller than the minute.
We use the second to tell a moment of time more accurately or precisely.

We use h to denote hour, min to denote minute and s to denote second.
1 minute = 60 seconds
1 min     = 60 s


clock showing 5 seconds, 35 seconds, 60 seconds


The 24-hour Clock

The following time line shows times in 24-hour clock and 12-hour clock.

time line showing 24-hour and 12-hour clocks

Rachel leaves home for school at 6.45 in the morning.

morning 6.45
a.m. is the period from midnight to noon.

Using the 12-hour clock, we write this time as 6.45 a.m. and read it as six forty-five a.m.

Using the 24-hour clock, we write this time as 06 45 and read it as zero six forty-five hours.


Rachel returns home from school at 2.25 in the afternoon.

afternoon 2.25
p.m. is the period from noon to midnight.

Using the 12-hour clock, we write this time as 2.25 p.m. and read it as two twenty-five p.m.

Using the 24-hour clock, we write this time as 14 25 and read it as fourteen twenty-five hours.

We add 12 hours to the 12-hour clock time in p.m. to change it to 24-hour clock time.
Example: Express 3.45 p.m. using the 24-hour clock.
3 + 12 = 15
3.45 p.m. is 15 45 in the 24-hour clock.

We subtract 12 hours from 24-hour clock time to change it to the 12-hour clock time in p.m.
Example: Express 20 30 using the 12-hour clock.
20 − 12 = 8
20 30 is 8.30 p.m. in the 12-hour clock.


Problem 1

In the clock below, where should the missing second hand be at?

place the missing second hand


35 seconds later, the missing second hand of the clock will be at the position shown below.

place the missing second hand


Problem 2

Find the duration.


finding duration in seconds


The first clock shows a time of 7.45 and 50 s. The second clock shows a time of 7.46 and 15 s.

From 7.45 and 50 s to 7.46, the duration is 10 s.
From 7.46 to 7.46 and 15 s, the duration is 15 s.

10 s + 15 s = 25 s
The duration between the two times is 25 s.


Problem 3

The following table shows how Dennis spent last Sunday. Complete the table using the 24-hour clock or the 12-hour clock as appropriate.

ActivityTime
24-hour clock12-hour clock
Wake up07 307.30 a.m.
Breakfast 8.00 a.m.
Community tree planting09 15 
Lunch12 00 
Watching TV 12.45 p.m.
Nap 1.15 p.m.
Story-telling with friends15 00 
Soccer16 30 
Dinner 6.30 p.m.
Iron school uniform19 30 
Movie20 00 
Bed time 9.30 p.m.


Here's the completed table:

ActivityTime
24-hour clock12-hour clock
Wake up07 307.30 a.m.
Breakfast08 008.00 a.m.
Community tree planting09 159.15 a.m.
Lunch12 0012.00 p.m.
Watching TV12 4512.45 p.m.
Nap13 151.15 p.m.
Story-telling with friends15 003.00 p.m.
Soccer16 304.30 p.m.
Dinner18 306.30 p.m.
Iron school uniform19 307.30 p.m.
Movie20 008.00 p.m.
Bed time21 309.30 p.m.

Problem 4

Derek started typing a composition at 09 30 and finished typing at 10 45. How long did he take to type the composition?
    a)   Express your answer in minutes.
    b)   Express your answer in hours and minutes.

start and end times with duration in 24-hour clock

a) From 09 30 to 10 45, the duration is 1 h 15 min.
    Derek took 1 h 15 min to type the composition.

b) From 09 30 to 10 45, the duration is 75 minutes.
    Derek took 75 minutes to type the composition.


Problem 5

Mikey entered the library at 16 45 and left 1 h 30 min later. At what time did he leave the library?
    a)   Express your answer in 12-hour clock.
    b)   Express your answer in 24-hour clock.

30 min = 15 min + 15 min
start and end times with duration in 24-hour clock

a) 1 h 30 min after 16 45 is 18 15.
    Using 24-hour clock, he left the library at 18 15.

b) 18 15 is 6.15 p.m. in 12-hour clock.
    Using 12-hour clock, he left the library at 6.15 p.m.

Problem 6

The train from Sunshine City to Moonlight City took 2-1/2 h. If it left Sunshine City at 10.30 a.m., what time did it reach Moonlight City?
    a)   Express your answer in 12-hour clock.
    b)   Express your answer in 24-hour clock.

start and end times with duration in 12-hour clock

2 h after 10.30 a.m. is 12.30 p.m.
1
2
 h after 12.30 p.m. is 1.00 p.m.

a) 2-1/2 h after 10.30 a.m. is 1.00 p.m.
    Using 12-hour clock, the train reached Moonlight City at 1.00 p.m.

b) 1.00 p.m. is 13 00 in 24-hour clock.
    Using 24-hour clock, the train reached Moonlight City at 13 00.

Problem 7

Rayan took an overnight flight from Mumbai to Singapore. The flight took 5 h 40 min to arrive in Singapore at 04 15. At what time did the flight leave Mumbai?

Count backwards.
40 min = 15 min + 25 min
start and end times with duration in 24-hour clock

5 h 40 min before 04 15 is 22 35.
The flight left Mumbai at 22 35.