128. Time Units, Time Formats and Time Zones

Learning Intentions

convert between different units of time
convert between times in 24-hour time and a.m./p.m.
use a time zone map to relate times in different locations in the world

Pre-requisite Summary

Know that time is measured in units such as seconds, minutes and hours
Know that $1$ minute $= 60$ seconds and $1$ hour $= 60$ minutes
Know that there are $24$ hours in a day
Be able to read analogue and digital times
Understand the meaning of a.m. and p.m.
Know that places around the world can have different local times
Be able to add and subtract whole numbers when calculating time differences
Understand that a time zone map shows offsets from a reference time

Worked Examples

Worked Example 1

Convert between units of time:
a) $3$ hours to minutes
b) $150$ minutes to hours and minutes
c) $2$ days to hours

Worked Example 2

Convert between units of time:
a) $360$ seconds to minutes
b) $5$ weeks to days
c) $48$ hours to days

Worked Example 3

Convert between 24-hour time and a.m./p.m.:
a) $07 : 45$
b) $14 : 20$
c) $12 : 00$

Worked Example 4

Convert between 24-hour time and a.m./p.m.:
a) $9 : 15$ p.m.
b) $12 : 30$ a.m.
c) $6 : 05$ a.m.

Worked Example 5

Use a time zone map to relate times:
a) If it is $3 : 00$ p.m. in London and Tokyo is $9$ hours ahead, what time is it in Tokyo?
b) If it is $8 : 00$ a.m. in Sydney and Perth is $2$ hours behind, what time is it in Perth?

Worked Example 6

Use a time zone map to relate times:
a) If it is $11 : 00$ a.m. in Brisbane and Auckland is $2$ hours ahead, what time is it in Auckland?
b) If it is $6 : 00$ p.m. in New Delhi and Dubai is $1.5$ hours behind, what time is it in Dubai?

Problems

Problem 1

Convert between units of time:
a) $4$ hours to minutes
b) $190$ minutes to hours and minutes
c) $3$ days to hours

Problem 2

Convert between units of time:
a) $420$ seconds to minutes
b) $6$ weeks to days
c) $72$ hours to days

Problem 3

Convert between 24-hour time and a.m./p.m.:
a) $06 : 30$
b) $17 : 50$
c) $00 : 00$

Problem 4

Convert between 24-hour time and a.m./p.m.:
a) $8 : 40$ p.m.
b) $12 : 15$ p.m.
c) $5 : 25$ a.m.

Problem 5

Use a time zone map to relate times:
a) If it is $4 : 00$ p.m. in London and Paris is $1$ hour ahead, what time is it in Paris?
b) If it is $9 : 00$ a.m. in Melbourne and Adelaide is $0.5$ hours behind, what time is it in Adelaide?

Problem 6

Use a time zone map to relate times:
a) If it is $10 : 00$ a.m. in Brisbane and Wellington is $2$ hours ahead, what time is it in Wellington?
b) If it is $7 : 00$ p.m. in Singapore and Bangkok is $1$ hour behind, what time is it in Bangkok?

Exercises

Understanding and Fluency

Complete each statement:
a) $1$ minute $= \underset{―}{}$ seconds
b) $1$ hour $= \underset{―}{}$ minutes
c) $1$ day $= \underset{―}{}$ hours
d) $1$ week $= \underset{―}{}$ days
Convert between units of time:
a) $5$ hours to minutes
b) $240$ minutes to hours
c) $180$ seconds to minutes
d) $2$ weeks to days
Convert between units of time:
a) $90$ minutes to hours and minutes
b) $150$ seconds to minutes and seconds
c) $36$ hours to days and hours
d) $10$ days to hours
Convert each 24-hour time to a.m./p.m.:
a) $08 : 15$
b) $13 : 40$
c) $19 : 05$
d) $00 : 30$
Convert each a.m./p.m. time to 24-hour time:
a) $7 : 20$ a.m.
b) $2 : 55$ p.m.
c) $12 : 10$ a.m.
d) $11 : 45$ p.m.
Use the given time zone difference to find the new time:
a) It is $6 : 00$ p.m. in Brisbane. Sydney is $1$ hour ahead. What time is it in Sydney?
b) It is $9 : 00$ a.m. in Perth. Brisbane is $2$ hours ahead. What time is it in Brisbane?
c) It is $3 : 30$ p.m. in Adelaide. Darwin is $0.5$ hours behind. What time is it in Darwin?
Use the given time zone difference to find the new time:
a) It is $1 : 00$ p.m. in London. Rome is $1$ hour ahead. What time is it in Rome?
b) It is $11 : 00$ a.m. in Tokyo. Seoul is in the same time zone. What time is it in Seoul?
c) It is $8 : 00$ p.m. in Dubai. Mumbai is $1.5$ hours ahead. What time is it in Mumbai?
Solve each:
a) A movie lasts $125$ minutes. Write this in hours and minutes
b) A flight leaves at $21 : 40$ . Write this in a.m./p.m. time
c) If it is $7 : 00$ a.m. in Brisbane and Auckland is $2$ hours ahead, what time is it in Auckland?

Reasoning

Explain why $14 : 00$ in 24-hour time is the same as $2 : 00$ p.m.
A student says that $12 : 00$ a.m. is midday. Explain the mistake.
Noah says that if one city is $3$ hours ahead, you subtract $3$ hours from the time. Is he correct? Explain.
Explain why a time zone map is useful when comparing times in different countries.
A student says that $90$ minutes is $0.9$ hours because the digits look similar. Describe the error.

Problem-solving

A train journey lasts $185$ minutes. Write the journey time in hours and minutes.
A concert starts at $18 : 45$ . Write this in a.m./p.m. time.
If it is $10 : 00$ a.m. in Brisbane and Tokyo is $1$ hour behind, what time is it in Tokyo?
If it is $4 : 30$ p.m. in New York and Los Angeles is $3$ hours behind, what time is it in Los Angeles?
A live event is shown at $7 : 00$ p.m. in London. If Johannesburg is $1$ hour ahead, what time is it there?
A lesson begins at $8 : 15$ a.m. and lasts $95$ minutes. What time does it finish, written in 24-hour time?

Potential Misunderstandings

Students may confuse the conversion facts for seconds, minutes and hours
Students may divide when they should multiply, or multiply when they should divide, when converting time units
Students may think $100$ minutes equals $1$ hour because of the base- $10$ number system
Students may confuse a.m. and p.m.
Students may think $12 : 00$ a.m. is noon instead of midnight
Students may think $12 : 00$ p.m. is midnight instead of noon
Students may forget to add $12$ when converting p.m. times to 24-hour time after midday
Students may incorrectly write $00 : 00$ as $0 : 00$ p.m.
Students may add or subtract time zone differences in the wrong direction
Students may ignore half-hour time differences on a time zone map
Students may forget to adjust the day when a time crosses midnight