Time intervals and time zones booklet
Time intervals and time zones booklet
- Unit 1: Numbers
- Unit 2: Geometry and measure
- Unit 3: Statistics and probability
🎯 In this topic you will
- Explore time intervals shorter than one second
- Calculate time intervals accurately
- Compare times across different time zones
🧠 Key Words
- time interval
- time zone
- Universal Time (UT)
Show Definitions
- time interval: The amount of time between two moments or events.
- time zone: A region of the world that uses the same standard time.
- Universal Time (UT): The global time standard based on Earth's rotation, used to coordinate time worldwide.
Using Time in Everyday Life
T ime and time intervals are used in many places every day. Trains and buses often follow a timetable, allowing us to calculate how long a journey will take or how long we will need to wait at a station.
Checking Times Around the World
W hen we want to contact people in other countries through the internet or by telephone, we can look at the time difference to check whether they will be awake.
Understanding Universal Time
S tandard time around the world is based on Universal Time (UT), measured at Greenwich, England. Each 15° of longitude away from Greenwich corresponds to a 1-hour time difference. Actual time zones often vary from this because of country borders and regional choices.
❓ EXERCISE 16.1 – Time intervals and time zones
1. Describe an activity that takes approximately:
a. $0.5$ seconds
b. $5$ seconds
c. $0.5$ minutes
d. $5$ minutes
👀 Show answer
Answers will vary. Example answers:
• $0.5$ seconds: blinking your eyes.
• $5$ seconds: taking a short drink of water.
• $0.5$ minutes ($30$ seconds): tying one shoe lace.
• $5$ minutes: brushing your teeth.
2. These are the times that six motorbike riders took to travel around a race track.
| Bike number | Rider's name | Time (seconds) |
|---|---|---|
| $1$ | Markus | $52.6$ |
| $2$ | Eduardo | $51.5$ |
| $3$ | Francis | $53.4$ |
| $4$ | Daniel | $53.1$ |
| $5$ | Leke | $52.3$ |
| $6$ | Amir | $52.9$ |
a. Which rider was the fastest?
b. Which rider was the slowest?
c. Write all the times in order from fastest to slowest.
Check your partner's answers for question $2$.
Talk to your partner about whether their answers show that they:
• can compare two times
• understand that the lowest number is the fastest time and the highest number is the slowest time.
👀 Show answer
a. The fastest rider is Eduardo with a time of $51.5$ seconds.
b. The slowest rider is Francis with a time of $53.4$ seconds.
c. Times in order from fastest to slowest:
Eduardo $51.5$ s, Leke $52.3$ s, Markus $52.6$ s, Amir $52.9$ s, Daniel $53.1$ s, Francis $53.4$ s.
These answers show that you can compare two times and that a lower time means faster and a higher time means slower.
3. Arun says, "I balanced on one leg for $2$ minutes and $23$ seconds." Zara says, "I balanced on one leg for $132$ seconds."
a. Who balanced on one leg the longest?
b. Work with a partner to time how long you can balance on one leg. Write the time using minutes and seconds and write it again using only seconds.
👀 Show answer
a. Convert Arun's time to seconds:
$2$ minutes $23$ seconds $= 2 \times 60 + 23 = 120 + 23 = 143$ seconds.
Zara's time is $132$ seconds.
Since $143 > 132$, Arun balanced on one leg for longer.
b. Answers will vary. Example: if you balanced for $1$ minute $30$ seconds, that is:
$1$ minute $30$ seconds $= 1 \times 60 + 30 = 90$ seconds.
4. Copy and complete the table to show the number of hours in each number of days.
| Number of days | Number of hours |
|---|---|
| $0.5$ | |
| $1$ | $24$ |
| $1.5$ | |
| $2$ | |
| $2.5$ | |
| $3$ |
👀 Show answer
There are $24$ hours in $1$ day, so multiply the number of days by $24$:
$0.5$ days: $0.5 \times 24 = 12$ hours
$1$ day: $24$ hours (given)
$1.5$ days: $1.5 \times 24 = 36$ hours
$2$ days: $2 \times 24 = 48$ hours
$2.5$ days: $2.5 \times 24 = 60$ hours
$3$ days: $3 \times 24 = 72$ hours
Use this timetable to answer questions $5$ to $8$.
| Train timetable | A | B | C |
|---|---|---|---|
| Ourtown | $10{:}11$ | $12{:}32$ | $14{:}23$ |
| Riverton | $10{:}47$ | $13{:}08$ | $14{:}59$ |
| Hillbury | $11{:}17$ | $13{:}38$ | $15{:}29$ |
| Newcity | $12{:}32$ | $14{:}53$ | $16{:}44$ |
5. How long does it take for the train to travel:
a. from Ourtown to Riverton?
b. from Hillbury to Newcity?
c. from Ourtown to Hillbury?
d. from Ourtown to Newcity?
👀 Show answer
The journey times are the differences between the arrival and departure times for the same train.
a. Ourtown to Riverton:
$10{:}47 - 10{:}11 = 36$ minutes. So it takes $36$ minutes.
b. Hillbury to Newcity:
$12{:}32 - 11{:}17 = 75$ minutes $= 1$ hour $15$ minutes.
c. Ourtown to Hillbury:
$11{:}17 - 10{:}11 = 66$ minutes $= 1$ hour $6$ minutes.
d. Ourtown to Newcity:
$12{:}32 - 10{:}11 = 141$ minutes $= 2$ hours $21$ minutes.
6. How long do I have to wait for a train if I arrive at:
a. Ourtown station at $09{:}42$?
b. Riverton station at $10{:}58$?
c. Hillbury station at $13{:}17$?
d. Riverton station at $14{:}36$?
👀 Show answer
For each station, find the next train time after the arrival time and subtract.
a. Ourtown: next train after $09{:}42$ is at $10{:}11$.
Wait time $= 10{:}11 - 09{:}42 = 29$ minutes.
b. Riverton: next train after $10{:}58$ is at $13{:}08$.
Wait time $= 13{:}08 - 10{:}58 = 130$ minutes $= 2$ hours $10$ minutes.
c. Hillbury: next train after $13{:}17$ is at $13{:}38$.
Wait time $= 13{:}38 - 13{:}17 = 21$ minutes.
d. Riverton: next train after $14{:}36$ is at $14{:}59$.
Wait time $= 14{:}59 - 14{:}36 = 23$ minutes.
7. Which is the latest train I can catch from Ourtown to arrive at:
a. Riverton station by $12{:}00$?
b. Hillbury station by $14{:}15$?
c. Newcity station by $15{:}30$?
d. Hillbury station by $15{:}40$?
👀 Show answer
Check which trains arrive by the required time and choose the latest departure from Ourtown.
a. Riverton by $12{:}00$:
Arrivals at Riverton are $10{:}47$, $13{:}08$, $14{:}59$. Only train A ($10{:}47$) arrives by $12{:}00$.
Latest train: Train A leaving Ourtown at $10{:}11$.
b. Hillbury by $14{:}15$:
Arrivals at Hillbury are $11{:}17$, $13{:}38$, $15{:}29$. Trains A and B arrive by $14{:}15$.
Latest train: Train B leaving Ourtown at $12{:}32$.
c. Newcity by $15{:}30$:
Arrivals at Newcity are $12{:}32$, $14{:}53$, $16{:}44$. Trains A and B arrive by $15{:}30$.
Latest train: Train B leaving Ourtown at $12{:}32$.
d. Hillbury by $15{:}40$:
Arrivals at Hillbury are $11{:}17$, $13{:}38$, $15{:}29$ — all are before $15{:}40$.
Latest train: Train C leaving Ourtown at $14{:}23$.
8. Tara takes train C to Newcity. She arrives at Newcity station then walks home for $20$ minutes. At what time does she arrive home?
👀 Show answer
Train C arrives at Newcity at $16{:}44$.
She then walks home for $20$ minutes:
$16{:}44 + 20$ minutes $= 17{:}04$.
So Tara arrives home at $17{:}04$.
The world is divided into $24$ time zones. This is a simple map showing approximate time zones. It shows how far ahead or behind the time is in hours from the Universal Time at '0'.
Many land time zone lines are moved to give countries a manageable time system. Some countries cross more than one time zone. Use this map to answer questions $9$ to $11$.
9. What is the approximate time difference in hours between:
a. Quito and Lagos?
b. Anchorage and Colombo?
c. Cape Town and Ulaanbaatar?
d. Nouakchott and Sydney?
👀 Show answer
Using the time zone map (approximate offsets from Universal Time):
Quito $\approx -5$, Lagos $\approx +1$ → difference $= 6$ hours.
Anchorage $\approx -9$, Colombo $\approx +6$ → difference $= 15$ hours.
Cape Town $\approx +2$, Ulaanbaatar $\approx +8$ → difference $= 6$ hours.
Nouakchott $\approx 0$, Sydney $\approx +10$ → difference $= 10$ hours.
a. $6$ hours
b. $15$ hours
c. $6$ hours
d. $10$ hours
10. Use the map to estimate.
a. If it was $09{:}21$ in Lagos, what would be the time in Omsk?
b. If it was $01{:}44$ in Acapulco, what would be the time in Port Moresby?
c. If it was $18{:}03$ in Rio de Janeiro, what would be the time in Ankara?
d. If it was $20{:}18$ in Manila, what would be the time in Colombo?
👀 Show answer
Approximate time zone offsets:
Lagos $\approx +1$, Omsk $\approx +6$ (Omsk is $5$ hours ahead of Lagos).
Acapulco $\approx -6$, Port Moresby $\approx +10$ (Port Moresby is $16$ hours ahead of Acapulco).
Rio de Janeiro $\approx -3$, Ankara $\approx +2$ (Ankara is $5$ hours ahead of Rio).
Manila $\approx +8$, Colombo $\approx +6$ (Colombo is $2$ hours behind Manila).
a. $09{:}21 + 5$ hours $= 14{:}21$ in Omsk.
b. $01{:}44 + 16$ hours $= 17{:}44$ in Port Moresby (next day).
c. $18{:}03 + 5$ hours $= 23{:}03$ in Ankara.
d. $20{:}18 - 2$ hours $= 18{:}18$ in Colombo.
11. If it was midday in Abu Dhabi, which cities on the map would have a different date to the date in Abu Dhabi?
👀 Show answer
Abu Dhabi is approximately at time zone $+4$.
Cities more than $12$ hours behind or ahead of Abu Dhabi will have a different date.
Anchorage is about $-9$, which is $13$ hours behind Abu Dhabi, so the local time there would be on the previous day.
Therefore, the city with a different date is:
Anchorage.
🧠 Think like a Mathematician
Scenario: Sofia, Zara, Arun and Marcus have all answered this question:
Question: Amy called Eva on the telephone at $18{:}35$ in Amy's country. Eva's time zone is $5$ hours ahead ($+5$) of Amy's time zone. They spoke on the telephone for $48$ minutes. What was the time for Eva when the call finished?
Their answers are:
- Sofia:$14{:}23$
- Zara:$19{:}23$
- Arun:$23{:}83$
- Marcus:$00{:}23$
Investigation task (work on your own):
- Work out the correct time for Eva when the call finished.
- Compare your answer with the four children's answers above and decide whose answer is correct.
- For each incorrect answer, think carefully about what mistake the child might have made in their calculations.
- Write feedback to each child who got the question incorrect. Explain where they went wrong and how they could change their method to get the answer right next time.
Thinking prompts:
- You are critiquing when you think about the mistakes each child might have made.
- You are convincing when you explain clearly where each child went wrong.
- You are improving when you suggest how each child could get the answer right next time.
👀 show answer
- 1. Correct time for Eva:
Amy starts the call at $18{:}35$. Eva's time is $5$ hours ahead, so when the call starts for Eva it is:
$18{:}35 + 5\text{ h} = 23{:}35$.
They talk for $48$ minutes:
$23{:}35 + 48\text{ min} = 23{:}(35+48) = 23{:}83$.
$83$ minutes is $1$ hour and $23$ minutes, so this is $24{:}23 = 00{:}23$ (the next day).
So Eva's correct finishing time is $00{:}23$. - 2. Which child is correct?
Marcus's answer, $00{:}23$, is correct. - 3. Likely mistakes in the incorrect answers:
Sofia – $14{:}23$: she seems to have subtracted the $5$-hour time difference instead of adding it, and then added the $48$ minutes. In other words, she treated Eva as being behind Amy instead of ahead.
Zara – $19{:}23$: she correctly added the $48$ minutes to Amy's time, but she did not change to Eva's time zone at all. She just found the time when the call finished in Amy's country.
Arun – $23{:}83$: he seems to have added the $5$-hour time difference and the $48$ minutes correctly, but left his answer as $23{:}83$ instead of converting $83$ minutes into $1$ hour and $23$ minutes. - 4. Example feedback to improve each incorrect answer:
Sofia: "Eva is $5$ hours ahead of Amy, so you should add $5$ hours to Amy's time, not subtract. Start from $18{:}35$, add $5$ hours to get $23{:}35$, then add the $48$ minutes."
Zara: "You correctly added the $48$ minutes, but you forgot to change the time to Eva's time zone. After finding $19{:}23$ for Amy, add another $5$ hours to get Eva's time, then adjust for minutes."
Arun: "Your method is almost correct. You must remember that there are only $60$ minutes in an hour. When you get $23{:}83$, convert $83$ minutes into $1$ hour and $23$ minutes to make $00{:}23$ on the next day."