12-hour clock to 24-hour clock
Morning (a.m.)
12:18 a.m.00 18
9:14 a.m.09 14
11:32 a.m.11 32
Afternoon / evening (p.m.)
12:10 p.m.12 10
2:22 p.m.14 22
6:55 p.m.18 55
11:05 p.m.23 05
For p.m. times from 1 p.m. to 11:59 p.m., add 12 to the hour.
Chapter 15
Time
Master 24-hour time, add and subtract time confidently, read timetables, convert between ordinary and decimal time, and solve time-zone problems with clear step-by-step methods.
By the end of this chapter, you should be able to
- convert between the 12-hour and 24-hour clock;
- add and subtract times in hours, minutes and seconds;
- interpret and use timetables correctly, including journeys that pass midnight;
- convert between hours and minutes and hours written as decimals;
- use time calculations in speed questions;
- solve simple time-zone problems by working with local-time differences.
1
Subtopic 1
The 24-hour clock
Times of day can be written using a.m., p.m., or the 24-hour clock. Morning times keep the same hour number, while afternoon times usually add 12 to the hour number.
24-hour day line
00 00midnight
06 00morning
12 00midday
18 00evening
23 59end of day
00–11a.m.
12noon / p.m.
13–23p.m.
Times between midnight and 1 a.m. start with 00.
Quick rules
- To change a.m. to 24-hour time, keep the hour the same (add a zero at the start if needed).
- To change p.m. to 24-hour time, add 12 to the hour, except for 12 noon.
- To change 24-hour time to 12-hour time, subtract 12 from afternoon/evening times and add p.m.
Worked example · Easy
12-hour to 24-hour time
Write 6.45 p.m. using the 24-hour clock.
Because it is a p.m. time, add 12 to the hour:
\[6+12=18\]So the time is \(\boxed{18\ 45}\).
Worked example · Medium
24-hour to 12-hour time
Write \(21\ 17\) using a.m./p.m. notation.
21 is after 12, so subtract 12.
\[21-12=9\]So \(21\ 17\) is \(\boxed{9.17\text{ p.m.}}\).
Worked example · Exam-style
Midnight trap
Write 12.08 a.m. and 12.08 p.m. using the 24-hour clock.
12.08 a.m. is just after midnight, so it is \(\boxed{00\ 08}\).
12.08 p.m. is just after midday, so it is \(\boxed{12\ 08}\).
Common mistake
Do not write 12.30 p.m. as 24 30. Noon stays in the 12th hour: 12 30.
Remember for this subtopic
Write 24-hour times using four digits: 00:00 is midnight and 12:00 is noon. For p.m. times except 12 p.m., add 12 to the hour; for a.m. times except 12 a.m., keep the hour.
Worked example · Exam-style
A change from p.m. to a.m.
A bus leaves at 11:45 p.m. and reaches a stop at 12:20 a.m. Write these times in 24-hour notation.
Step-by-step solution
11:45 p.m. is \(23{:}45\); 12:20 a.m. is \(00{:}20\) on the next day. Answer: \(\boxed{23{:}45\text{ and }00{:}20}\).
Progressive practice: confidence to exam-style
Try each question before opening the solution. Exam-style questions are original and modelled on the skills tested in examinations.
1Easy practice [1 marks]
Write 7:05 a.m. in 24-hour notation.
Show Answer
Step-by-step solution
Before 10 a.m., add a leading zero: 07:05.
2Medium practice [2 marks]
Write 9:40 p.m. in 24-hour notation.
Show Answer
Step-by-step solution
Add 12 to 9: 21:40. Answer: 21:40.
3Medium practice [3 marks]
Write 00:18 in 12-hour notation.
Show Answer
Step-by-step solution
The hour 00 is midnight: 12:18 a.m.
4Exam-style practice [4 marks]
A timetable shows a bus leaving at 14:05. Write the time on a 12-hour clock.
Show Answer
Step-by-step solution
14−12=2, so the time is 2:05 p.m.
2
Subtopic 2
Calculating with time
When adding or subtracting time, remember that 60 minutes = 1 hour and 60 seconds = 1 minute. In harder questions, it helps to draw a timeline or break the journey into parts.
Adding time
15 min25 min
7.45 a.m.8.00 a.m.8.25 a.m.
Split 40 minutes into 15 minutes to the next hour, then 25 more minutes.
Finding a duration
40 min1 h 10 min
15 2016 0017 10
Move to the next full hour first, then continue.
Worked example · Easy
Add minutes to a time
Mavis leaves for school at 7.45 a.m. and arrives 40 minutes later. At what time does she arrive?
From 7.45 a.m. to 8.00 a.m. is 15 minutes.
There are \(40-15=25\) minutes left.
So the arrival time is \(\boxed{8.25\text{ a.m.}}\).
Worked example · Medium
Find a duration
A digital recorder starts at \(15\ 20\) and stops at \(17\ 10\). For how long does it record?
From \(15\ 20\) to \(16\ 00\) is 40 minutes.
From \(16\ 00\) to \(17\ 10\) is 1 hour 10 minutes.
Total time = \(1\text{ h }50\text{ min}\).
Answer: \(\boxed{1\text{ hour }50\text{ minutes}}\).
Worked example · Medium
Work backwards
Nathee is ready to start cooking at 6.15 p.m. It took 35 minutes to prepare the food. At what time did he start preparing it?
15 minutes before 6.15 p.m. is 6.00 p.m.
There are \(35-15=20\) minutes still to go back.
20 minutes before 6.00 p.m. is \(\boxed{5.40\text{ p.m.}}\).
Worked example · Exam-style
Crossing midnight
A coach leaves at \(23\ 35\) and arrives 2 hours 40 minutes later. Find the arrival time.
From \(23\ 35\) to \(24\ 00\) is 25 minutes.
That leaves 2 hours 15 minutes.
2 hours after midnight is \(02\ 00\), then 15 minutes more gives \(\boxed{02\ 15}\).
Remember for this subtopic
To subtract times, calculate total minutes or use a number-line working across whole hours. For a timetable, compare the displayed departure and arrival times and check whether arrival is on the next day.
Worked example · Exam-style
Journey time across midnight
A coach leaves at 22:35 and arrives at 01:15 next day. How long is the journey?
Step-by-step solution
22:35→24:00 is 1 h 25 min. 00:00→01:15 is 1 h 15 min. Total \(\boxed{2\text{ h }40\text{ min}}\).
Progressive practice: confidence to exam-style
Try each question before opening the solution. Exam-style questions are original and modelled on the skills tested in examinations.
1Easy practice [1 marks]
A train leaves at 08:20 and arrives at 10:05. Find the journey time.
Show Answer
Step-by-step solution
08:20→09:00 = 40 min; 09:00→10:05 = 65 min. Total 105 min = 1 h 45 min.
2Medium practice [2 marks]
Add 2 hours 35 minutes to 13:50.
Show Answer
Step-by-step solution
13:50 + 2 h = 15:50; +35 min = 16:25.
3Medium practice [3 marks]
A ferry takes 1 h 55 min and must arrive by 18:10. Find its departure time.
Show Answer
Step-by-step solution
18:10 − 1 h = 17:10; −55 min = 16:15.
4Exam-style practice [4 marks]
A flight leaves at 23:48 and lands at 03:12 on the next day. Find the time in the air.
Show Answer
Step-by-step solution
23:48→24:00 = 12 min. 00:00→03:12 = 3 h 12 min. Total 3 h 24 min.
4
Subtopic 4
Converting between hours and minutes and hours written as a decimal
In speed and calculator questions, time is often written as a decimal number of hours. To work accurately, you must be able to convert both ways.
Hours and minutes → decimal hours
5 h 37 min37 min = \(\frac{37}{60}=0.6166\ldots\) h5.6166… h
To convert minutes to hours, divide by 60.
Decimal hours → hours and minutes
15.36 h0.36 h × 60 = 21.6 min15 h 22 min
To convert decimal hours to minutes, multiply the decimal part by 60.
Worked example · Easy
Convert minutes to hours
Write 8 minutes 36 seconds in minutes.
36 seconds = \(\frac{36}{60}=0.6\) minutes.
So 8 minutes 36 seconds = \(8+0.6=\boxed{8.6\text{ minutes}}\).
Worked example · Medium
Convert decimal hours
Write 6.4 hours in hours and minutes.
The decimal part is 0.4 hours.
\[0.4\times60=24\text{ minutes}\]So the time is \(\boxed{6\text{ hours }24\text{ minutes}}\).
Worked example · Medium
Nearest minute
Write 15.36 hours in hours and minutes, correct to the nearest minute.
\[0.36\times60=21.6\text{ minutes}\]
21.6 minutes rounds to 22 minutes.
So the answer is \(\boxed{15\text{ h }22\text{ min}}\).
Worked example · Exam-style
Use decimal hours in a speed question
The Beijing to Shanghai train travels 1318 km in 5 hours 37 minutes. Find the average speed, correct to the nearest km/h.
Convert time to hours:
\[37\div60=0.6166\ldots\text{ h}\]\[5\text{ h }37\text{ min}=5.6166\ldots\text{ h}\]Now use speed = distance ÷ time:
\[\text{speed}=\frac{1318}{5.6166\ldots}=234.658\ldots\]To the nearest km/h, \(\boxed{235\text{ km/h}}\).
Remember for this subtopic
To change minutes to a decimal of an hour, divide by 60. To change the decimal part of an hour to minutes, multiply by 60. Never treat “1 h 45 min” as “1.45 h”.
Worked example · Exam-style
Use decimal hours to calculate speed
A train travels 135 km in 1 hour 48 minutes. Find its average speed in km/h.
Step-by-step solution
\(1\text{ h }48\text{ min}=1+48/60=1.8\text{ h}\). Speed \(=135/1.8=\boxed{75\text{ km/h}}\).
Progressive practice: confidence to exam-style
Try each question before opening the solution. Exam-style questions are original and modelled on the skills tested in examinations.
1Easy practice [1 marks]
Convert 42 min to hours, as a decimal.
Show Answer
Step-by-step solution
\(42\div60=\boxed{0.7\text{ h}}\).
2Medium practice [2 marks]
Write 2.25 h in hours and minutes.
Show Answer
Step-by-step solution
\(0.25\times60=15\). Answer \(\boxed{2\text{ h }15\text{ min}}\).
3Medium practice [3 marks]
Convert 1 hour 18 minutes to decimal hours.
Show Answer
Step-by-step solution
\(1+18/60=\boxed{1.3\text{ h}}\).
4Exam-style practice [4 marks]
A swimmer takes 0.625 hours. Express the time in minutes and seconds.
Show Answer
Step-by-step solution
\(0.625\times60=37.5\) min. So \(\boxed{37\text{ min }30\text{ s}}\).
5
Subtopic 5
Time zones
Different countries can have different local times. If one city is ahead, add hours to the other city’s time. If it is behind, subtract hours. In flight questions, first find the landing time in the departure city’s local time, then adjust to the destination’s local time.
Figure: cities ahead and behind
Islamabad11 00
+6 h
Sydney17 00
Tokyo21 00
−5 h
Dubai16 00
“Ahead” means add hours. “Behind” means subtract hours.
Figure: flight method
- Start with the departure time in the departure city.
- Add the flight time.
- You now have the landing time in the departure city’s local time.
- Add or subtract the time-zone difference to get the destination local time.
Worked example · Medium
Simple comparison
The local time in Sydney is 6 hours ahead of the local time in Islamabad. What time is it in Sydney when it is \(11\ 00\) in Islamabad?
Sydney is ahead, so add 6 hours.
\[11\ 00+6\text{ h}=\boxed{17\ 00}\]Worked example · Exam-style
Flight arrival time
An aircraft leaves Dubai at \(08\ 55\) local time and flies to Tokyo. The flight takes 9 hours 25 minutes. Local time in Tokyo is 5 hours ahead of Dubai. What is the local time in Tokyo when the aircraft lands?
First find the arrival time in Dubai time:
\(08\ 55+9\text{ h }25\text{ min}=18\ 20\).
Tokyo is 5 hours ahead, so add 5 hours:
\(18\ 20+5\text{ h}=\boxed{23\ 20}\).
Worked example · Exam-style
Find the time difference
An aircraft leaves Dubai at 01 50 local time and arrives in Sydney at 22 30 local time. The flight time is 13 hours 40 minutes. How many hours ahead of Dubai time is Sydney time?
Arrival time in Dubai time would be:
\(01\ 50+13\text{ h }40\text{ min}=15\ 30\).
Actual arrival local time in Sydney is \(22\ 30\).
The difference is \(22\ 30-15\ 30=\boxed{7\text{ hours}}\).
Remember for this subtopic
Use the difference between local times. Travelling east generally moves clocks ahead; west moves them back. In these questions, use the time-zone information supplied rather than assuming current real-world offsets.
Worked example · Exam-style
Flight and time-zone difference
City B is 4 hours ahead of City A. A flight leaves A at 19:10 and lasts 6 h 40 min. Find its arrival time in City B.
Step-by-step solution
A-time arrival \(19{:}10+6{:}40=01{:}50\) next day. Add 4 hours: \(\boxed{05{:}50\text{ next day in B}}\).
Progressive practice: confidence to exam-style
Try each question before opening the solution. Exam-style questions are original and modelled on the skills tested in examinations.
1Easy practice [1 marks]
City Q is 3 hours ahead of City P. If it is 10:00 in P, find time in Q.
Show Answer
Step-by-step solution
Add 3 hours: 13:00 in Q.
2Medium practice [2 marks]
City A is 5 hours behind City B. If time in B is 02:00 on Tuesday, find time in A.
Show Answer
Step-by-step solution
Subtract 5 hours: 21:00 Monday.
3Medium practice [3 marks]
A meeting starts at 16:30 in a city 2 hours ahead of Kuwait. Find its Kuwait time.
Show Answer
Step-by-step solution
Subtract 2 hours: 14:30 Kuwait time.
4Exam-style practice [4 marks]
An aircraft departs a city at 22:15, flies for 3 h 30 min and lands in a city 6 hours behind the departure city. State the arrival time and day.
Show Answer
Step-by-step solution
Departure-zone arrival = 01:45 next day. Move clocks back 6 hours: 19:45 on the departure day at destination.
Chapter 15 practice
Start with clock-format conversions, then build to timeline, timetable and time-zone questions. Keep answers hidden until you have attempted each question.
A. Build confidence
124-hour clock[3 marks]
Write these times using the 24-hour clock: a) 9.35 a.m. b) 2.08 p.m. c) 12.49 a.m.
Show Answer
a) \(\boxed{09\ 35}\)
b) Add 12, so \(\boxed{14\ 08}\)
c) Just after midnight, so \(\boxed{00\ 49}\)
212-hour clock[3 marks]
Write these times using a.m./p.m. notation: a) \(03\ 45\) b) \(14\ 56\) c) \(23\ 40\).
Show Answer
a) \(\boxed{3.45\text{ a.m.}}\)
b) \(14-12=2\), so \(\boxed{2.56\text{ p.m.}}\)
c) \(23-12=11\), so \(\boxed{11.40\text{ p.m.}}\)
3Forward in time[3 marks]
A train leaves at 14 40 and arrives 50 minutes later. What time does it arrive?
Show Answer
20 minutes takes us to 15 00, then 30 more minutes gives \(\boxed{15\ 30}\).
4Backward in time[3 marks]
A film ends at 8.50 p.m. and lasted 1 hour 45 minutes. What time did it start?
Show Answer
8.50 p.m. − 50 minutes = 8.00 p.m. There are still 55 minutes to subtract.
8.00 p.m. − 55 minutes = \(\boxed{7.05\text{ p.m.}}\).
B. Timetables and journeys
5Ferry journey[3 marks]
A ferry left Liverpool at 14 20 and arrived at Belfast at 21 05. How long did it take?
Show Answer
14 20 to 15 00 = 40 min; 15 00 to 21 00 = 6 h; 21 00 to 21 05 = 5 min.
Total = \(\boxed{6\text{ h }45\text{ min}}\).
6Arrival time[3 marks]
Kylie leaves home at 7.50 a.m. and takes 2 hours 45 minutes to reach her friend’s house. What time does she arrive?
Show Answer
7.50 a.m. + 10 min = 8.00 a.m.; 2 h 35 min remain.
8.00 a.m. + 2 h 35 min = \(\boxed{10.35\text{ a.m.}}\).
7Recorder[3 marks]
Joe sets his digital recorder to switch on at 8.35 p.m. and switch off at 10.20 p.m. How long is the recorder on?
Show Answer
8.35 p.m. to 9.00 p.m. = 25 min; 9.00 p.m. to 10.00 p.m. = 1 h; 10.00 p.m. to 10.20 p.m. = 20 min.
Total = \(\boxed{1\text{ h }45\text{ min}}\).
8Journey after midnight[4 marks]
A ferry leaves port at 08 35 on a 55-minute journey. It arrives 20 minutes late due to bad weather. What time does it arrive?
Show Answer
Scheduled arrival: \(08\ 35+55\text{ min}=09\ 30\).
20 minutes late means \(09\ 30+20\text{ min}=\boxed{09\ 50}\).
C. Decimal time
9Decimal hours to ordinary time[3 marks]
Write 3.26 hours in hours and minutes, correct to the nearest minute.
Show Answer
\[0.26\times60=15.6\text{ min}\]
15.6 min rounds to 16 min, so the answer is \(\boxed{3\text{ h }16\text{ min}}\).
10Ordinary time to decimal hours[3 marks]
Write 4 hours 15 minutes as a decimal number of hours.
Show Answer
\[15\div60=0.25\text{ h}\]
So the answer is \(\boxed{4.25\text{ h}}\).
11Minutes and seconds[3 marks]
Write 4.7 minutes in minutes and seconds.
Show Answer
The 0.7 minute part must be converted to seconds.
\[0.7\times60=42\text{ s}\]So the answer is \(\boxed{4\text{ min }42\text{ s}}\).
12Speed with decimal time[4 marks]
Soraya drives for 3 hours 17 minutes and travels 140 km. What is her average speed?
Show Answer
Convert the time to hours:
\[17\div60=0.2833\ldots\text{ h}\]\[3\text{ h }17\text{ min}=3.2833\ldots\text{ h}\]\[\text{speed}=\frac{140}{3.2833\ldots}=42.64\ldots\]So the average speed is about \(\boxed{42.6\text{ km/h}}\) or \(\boxed{43\text{ km/h}}\) to the nearest km/h.
D. Exam-style challenge
13Train arrival[5 marks]
A train travels at an average speed of 85 km/h. The journey distance is 495 km. The train leaves at 13 35. What time does it arrive? Give your answer to the nearest minute.
Show Answer
First find the time:
\[\text{time}=\frac{495}{85}=5.823529\ldots\text{ h}\]Convert the decimal part:
\[0.823529\ldots\times60=49.41\ldots\text{ min}\]So the journey takes about 5 h 49 min.
13 35 + 5 h 49 min = \(\boxed{19\ 24}\).
14Aircraft to London[5 marks]
An aircraft leaves Karachi at 11 35 local time to fly to London. The flight time is 8 hours 30 minutes. The time in London is 4 hours behind the time in Karachi. What is the local time in London when the aircraft arrives?
Show Answer
Arrival time in Karachi time:
\(11\ 35+8\text{ h }30\text{ min}=20\ 05\).
London is 4 hours behind, so subtract 4 hours:
\(20\ 05-4\text{ h}=\boxed{16\ 05}\) or \(\boxed{4.05\text{ p.m.}}\).
15Aircraft to Sydney[5 marks]
An aircraft leaves Dubai at 01 50 local time and arrives in Sydney at 22 30 local time. The flight time is 13 hours 40 minutes. How many hours ahead of Dubai time is Sydney time?
Show Answer
01 50 + 13 h 40 min = 15 30 in Dubai time.
But the local arrival time in Sydney is 22 30.
The difference is \(22\ 30-15\ 30=\boxed{7\text{ hours}}\).
16Time-zone reasoning[6 marks]
The local time in Dubai is 5 hours behind the local time in Tokyo. What time is it in Dubai when it is 21 00 in Tokyo? If a flight leaves Tokyo at 21 00 and lands 6 hours 20 minutes later, what is the landing time in Dubai local time?
Show Answer
Dubai is 5 hours behind Tokyo, so when it is 21 00 in Tokyo, it is \(\boxed{16\ 00}\) in Dubai.
The flight lands 6 h 20 min after 21 00 Tokyo time, so the arrival time in Tokyo time is \(03\ 20\) next day.
Dubai is still 5 hours behind, so subtract 5 hours: \(03\ 20-5\text{ h}=22\ 20\) on the previous day.
Landing time in Dubai local time: \(\boxed{22\ 20}\).
Chapter 15 high-grade checklist
Clock formats
I can move confidently between 12-hour and 24-hour time, including midnight and noon.
60, not 100
I remember that 1 hour = 60 minutes and 1 minute = 60 seconds when adding or subtracting time.
Timeline method
I can break a time calculation into jumps to the next hour or to the next day.
Timetables
I can find durations and arrival times from a timetable, even when the journey passes midnight.
Decimal time
I can convert ordinary time to decimal hours and back when solving speed questions.
Time zones
I first find the arrival time in the departure city’s local time, then adjust for the time-zone difference.