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- END UNIT 1 ASSIGNMENTOpened: Saturday, 27 May 2023, 12:00 PMDue: Monday, 29 May 2023, 12:00 AM
UNIT 8:Solving problems involving time intervals
8.1 Converting units of time
• In P4 we learnt units of time. We have various units of measuring
time. They include seconds (s), minutes (min) and hours.
• Hours, minutes and seconds are related. Fill in the table.
(a) Converting hours into minutes
Activity 8.11. From the clock face below, identify the hour and minute hands
How many minutes equal an hour? Explain
2. Convert the following hours into minutes. Then present your findings.(a) 3 hours (b) 4 hours
Tip: 1 hour is equal to 60 minutes. 1 h = 60 min
Example 8.1
A tourist took 6 hours in her visit to the animal park. How many minutes
did the tourist take in the park?
Solution
1 h = 60 minutes.6 h = 6 × 60 min = 360 min
Practice Activity 8.1
Convert the hours given below into minutes.
1. 2 hours 2. 6 1/2 hours 3. 14 hours
4. 5 h 5. 12 h 6. 22 h
7. In a cross-country, an athlete run for 2 hours. How many minutes did
the athlete run? Discuss the importance of participating in athletics.
8. A man drove a car for 5 1/4
hours from town A to town B. How much time
in minutes did it take him? Justify your answer.
9. A traditional music festival lasted for 3 1/2
hours. How many minutes
did the festival last? Why is it important to participate in traditional
music festival?
10. A teacher took her pupils to visit Akagera National Park for 6 hours.How long did their visit last in minutes? Explain your answer.
(b) Converting minutes into hours
Activity 8.2
Convert the following minutes into hours. Discuss the steps followed.(a) 360 minutes (b) 480 minutes
Tip: 60 minutes equals to one hour. 60 min = 1 h
Example 8.2
(a) A National drama festival lasted for 180 minutes. How many hours
is this?
(b) In a school, an annual general meeting lasted for 200 minutes.
Calculate the number of hours and minutes it took. Explain yourworking steps.
So 200 min is (200 ÷ 60) h
By dividing 200 by 60, we get 3 h and 20 min remained.Thus, 200 min = 3 h 20 min.
Practice Activity 8.2
1. Convert the following into hours.
(a) 120 min (b) 360 min (c) 840 min
(d) 420 min (e) 240 min (f) 720 min
2. Convert the following into hours and minutes. Explain your answers.
(a) 72 min (b) 130 min (c) 90 min
(d) 61 min (e) 190 min (f) 320 min
3. A football match took 100 min. How many hours and minutes did the
match take? Discuss your steps.
4. In a certain village, community work of cleaning the road took 425
minutes. How many hours and minutes did the work take? Why should
we participate in community work? Explain.
5. Some workers were managing a river. They took 725 min to finish
their work. How many hours and minutes did their work take? Explainyour steps. Why should we manage our rivers?
8.2 Converting hours into seconds
Activity 8.3
1. Get a real clockface.
2. Identify the seconds hand (the longest hand)
3. Carefully observe the time it takes the second hand to make one
minute.
4. Finally observe the number of seconds that it takes to make one hour.
Convert the following into seconds.
(a) 2 hours (b) 4 hours
What steps have you followed? Explain
Tip: From table,1 h = 60 min ,1 min = 60 s
Therefore 1 h = (60 × 60)s = 3 600 s.Conversion fact: 1 h = 3 600 s
Example 8.3
(a) Convert 3 h into seconds.
(b) A public meeting took 6 h 50 s. How many seconds was the publicmeeting?
Solution
(a) 3 h = (3 × 3 600) s = 10 800 s
(b) 6 h = 6 × 3 600 s = 21 600 s
The public meeting took 6 h 50 s.
Thus, 6 h 50 s = 21 600 s + 50 s= 21 650 s
Practice Activity 8.3
1. Convert the following into seconds.
(a) 112 hours (b) 5 hours (c) 1014 hours
2. Convert the following into seconds. Discuss your steps.
(a) 3 hours (b) 12 hours (c) 234 hours
3. A bus took 10 h 30 s to travel from Town A to Town B. Find the time
in seconds that the bus traveled between the two towns.
4, A farmer spent 6 h 57 s to plant maize in his farm. How much time in
seconds did the farmer take? Explain your steps to answer.
5. A tractor took 2 hours to dig a piece of land. Calculate how much time
the tractor took in seconds?
6. A church prayer session lasted for 3 1/2 hours in the morning. How manyseconds did the prayer session last? Why do people pray?
8.3 Changing days into hours
Activity 8.4
1. Discuss the number of hours that are there from Tuesday midnight
up to Wednesday midnight.
2. I went to camp on Monday 8.00 a.m. I came back on Friday at
8.00 a.m.
(a) How many days was I in the camp?(b) How many hours was I in the camp? Discuss your answer
Tip: There are 24 hours in one day. 1 day = 24 h
Example 8.4
(a) How many hours are in 5 days?
(b) Workers took 10 1/2
days to make terraces for controlling soil erosion.How many hours did the workers took?
Solution
(a) 1 day = 24 hours
So, 5 days = 5 × 24 h
= 120 h
Therefore, 5 days have 120 hours.
(b) 1 day = 24 hours
So, 1/2 day = 1/2× 24 hours
= 12 hours
10 days = 10 × 24 h
= 240 h
Workers took 10 1/2 days.
Therefore, 10 1/2 days = 12 h + 240 h= 252 hours.
Practice Activity 8.4
1. Find the number of hours in the following:
(a) 10 days (b) 15 days (c) 6 days (d) 4 days
(e) 11 days (f) 13 days (g) 11 1/2 days
2. Joyce became the best in her classroom performance. Her parents
then permitted her to visit and stayed at her uncle’s place for 14 days.
How many hours did Joyce spend at her uncle’s place? Why should you
work hard?
3. A National music festival took place over 5 1/2 days. How many hours is
this? Justify your answer.
4. Due to sickness, John was admitted to the hospital for 20 1/2 days. How
many hours did John stay in the hospital? Discuss importance of
hospitals.
5. An activity of making a road took one week in a certain place. Howmany hours did it take? Discuss why we should make roads.
8.4 Changing hours into days
Activity 8.5
(a) • How many hours are there from midnight to midday?
• How many hours are there from midday to midnight?
• How many hours are in 1 day? Discuss your findings.
(b) Now discuss and convert the following into days.
(i) 24 h (ii) 48 h (iii) 120 h(c) Present your findings.
Tip: A day has 24 hours. A day starts at midnight up to the next midnight.24 h = 1 day
Example 8.5
(a) How many days are in 144 hours?
(b) A marriage counsellor took 182 hours to counsel two couples andsolve marriage problem. How many days and hours were these?
Practice Activity 8.5
1. How many days are in
(a) 120 hours? (b) 216 hours?
(c) 720 hours? (d) 432 hours?
2. How many days and hours are in
(a) 571 hours? (b) 612 hours? (c) 520 hours?
(d) 192 hours? (e) 242 hours?
3. A youth camp took place over 312 hours. How many days did the camp
take? Explain your answer.
4. A tour took 249 hours to visit East African countries by bus. How
many days did the tour take? Explain your answer. Why should you
tour other countries?
5. A boarding school went for mid-term holidays for 144 hours. How
many days was the holiday? Discuss your answer.
6. A semi-desert place did not receive rain for 6 760 hours. How many
days was the place without rain? Explain your steps. Why should weconserve our environment?
8.5 Finding time intervals
Activity 8.6
(a) What time do you go to school in the morning? What time do you
go back home in the evening from school? Find the length of time
between the two events.
(b) Find the time between the sunrise and the sunset. Justify your
answer.
(c) How long is the time for your Mathematics lesson? Present youranswer.
Tip:
• Duration – Length of time in which a particular event takes place.
It is calculated as; Duration = Ending time – Starting time
• Starting and Ending time can be given different names. For example;
(a) For a journey starting time is departure time. Ending time is
arrival time.
(b) For a match of football, starting time is kick-off time. Endingtime is stoppage time.
Example 8.6
A doctor was on duty in hospital from 8.00 a.m. to 12.00 noon. How long
was she on for duty?
Solution
Method 1
We subtract
Duration = 12.00 – 8.00 = 4 hoursMethod 2
The time is 4 hours.
Tip: Duration can be addition of lengths of time. For example;
Duration from 8 a.m. to 2 p.m. is
(12 – 8) h + 2 h = (4 + 2) h = 6 h.Confirm this from the time number line above.
Practice Activity 8.6
1. How many hours are there from
(a) 9.00 a.m. to 3.00 p.m.? (b) 4.00 a.m. to 1.00 p.m.?
(c) 6.00 a.m. to 4.00 p.m.? (d) 7.00 a.m. to 6.00 p.m.?
2. A baby slept at 8.15 a.m. and woke up at 10.15 a.m. How long did the
baby sleep? Explain your answer.
3. A train left from one station at 10.45 a.m. It arrived at the next station
at 12.45 p.m.. Calculate the time it took from one station to the next.
4. A football match started at 2.00 p.m. and ended at 3.30 p.m. How long
did the match take? Discuss your answer.
5. A class had lessons from 9.45 a.m. to 11.45 a.m. How long did the
lessons take? Justify your answer.
6. A religious meeting started at 1.00 p.m. and ended at 6.30 p.m. How
long was the meeting? Why should we be religious? Present your
answer.
7. A mathematics lesson started at 10.00 a.m. and ended at 12.30 p.m.
Calculate the duration of the lesson. Discuss why we should study
Mathematics.
8.6 Addition involving time
Activity 8.7
• Study the questions below. Then answer the questions correctly.
(a) A car travelled from town A to town B in 2 hours. It then travelled
to town C in 3 hours. Find the total duration of travel.
(b) A meeting took 5 h 45 min in the morning and 1 h 25 min in the
afternoon. Find the duration for the meeting.
• Now add the following durations.
(i) 2 h + 3 h =
(ii) 5 h 45 min + 1 h 25 min = ____ h ___ min
(iii) 3 h 30 min + 6 h 30 min = ____ h ___ minExplain your answers
Example 8.7
(a) Add 6 h + 9 h
(b) A train traveled from town P to Q over 7 h 55 min. Then it traveled
to town R over 2 h 15 min. Find the total time taken to travel from
P to Q to R.
(c) A mathematics lesson started at 8.40 a.m.. It lasted for 1 h 20 min.
At what time did the lesson end?
Solution
(a) 6 h + 9 h = 15 hours
(b) Time taken = 7 h 55 min + 2 h 15 min
= (7 h + 2 h) + (55 min + 15 min)
= 9 h + 70 min. (Now 70 min = 1 h 10 min)
= 9 h + 1 h 10 min = (9 h + 1 h) + 10 min
= 10 h 10 min
(c) Starting time = 8.40 a.m., duration = 1 h 20 minEnding time = starting time + duration = 8.40 a.m. + 1 h 20 min
Note: 60 min = 1 h, so you carry over 1 h.
Practice Activity 8.7
Work out the following:
1. 2 h + 1 h
2. 6 h + 7 h
3. 1 h 30 min + 4 h 30 min = ___ h ___ min
4. 12 h 37 min + 3 h 48 min = ___ h ___ min
Work out the following. Discuss your steps.
5. 10 min 5 s + 30 min 5 s = ___ min ___ s
6. 14 h 18 min + 12 h 32 min = ___ day ___ h ___ min
7. In a car race, twenty cars drove from the first town to a second town.
The winner took 1 h 20 min to reach the second town. He then drove to
a third town in 1 h 45 min. Calculate the total time the winner drove.
8. We stayed in assembly for 20 minutes. We then took 30 minutes to
clean the school compound. Calculate the duration of the two events.
9. A meeting started at 11.45 a.m.. It went on for 1 hour 45 minutes.
What time did the meeting end? Explain your steps.
10. We went for lunch at 12.45 p.m. We took a 1 h 15 min lunch break.When did the lunch break end? Discuss your steps.
8.7 Subtraction involving time
Activity 8.8
Look at the following questions.
Work them out:
(a) 18 h 35 min – 11 h 45 min = _____ h ____ min
(b) 4 h – 1 h 30 min = _____ h ____ min
(c) A cross-country race ended at 12.35 p.m.. The duration of the race
was 2 h 10 min. At what time did the race begin?Present your answers.
Example 8.8
Work out:
(a) 9 h 15 min – 5 h 45 min = ____ h ____ min
(b) A meeting started at 8 a.m. It ended at 11 a.m. There was a health
break from 9 a.m. to 9.30 a.m.
(i) How long was meeting?
(ii) Find the duration of the break.
(c) An aircraft left Kigali for Kenya on Monday. It then came back to
Kigali and arrived at 12.40 a.m. on Tuesday. The journey had taken
total time of 4 h 45 min. At what time did the aircraft leave Kigali
for Kenya?
Solution
(a) 9 h 15 min – 5 h 45 min =
• Start with 15 min – 45 min. It is not possible. Borrow 1 h to have
60 min + 15 min = 75 min. So (75 – 45) min = 30 min.
• Remember you borrowed 1 h from 9 h. We have; 8 h – 5 h = 3 h.
Thus, 9 h 15 min – 5 h 45 min = 3 h 30 min.
(b) (i) Duration = Ending time – starting time
= 11 a.m. – 8 a.m. = 3 h(ii) 9.30 a.m. – 9 a.m. = 30 min
We subtract 4 h from 12.40 a.m..
We stop at 8.40 p.m. previous day (Monday).
We now have 8.40 p.m. – 45 min = 7.55 p.m.The aircraft left Kigali at 7.55 p.m. on Monday.
Practice Activity 8.8
Work out the following.
1. 4 h – 2 h = 2. 8 h – 5 h =
3. 32 h 20 min – 20 h 10 min = ____ h ____ min
Work out the following. Explain your steps.
4. 16 h 30 min – 12 h 45 min = ____ h ____ min
5. 6 days 12 h – 3 days 9 h = ____ days ____ h
6. A volleyball match ended at 11.15 a.m. It was 3 h 20 min long. At what
time did the match start?
7. A football match stopped at 7.15 p.m. in Amahoro Stadium. It was
2 h 26 min long. Discuss what time the match started?
8. A taxi took a total of 3 h from the time it left the airport to Kigali city.
The taxi had stopped at a restaurant for 1 h 40 min for lunch.
(a) Calculate the travel time of the taxi.
(b) Solve: 3 h – 1 h 40 min = ___ h ___ min
9. A train arrived in a certain town at 4.30 p.m. It had taken 10 h 20 min
of travel from the previous station. What time had it departed from
the previous station? Discuss.10. Work out 18 h 15 min – 4 h 38 min = ___ h ___ min. Present your
answer.
1. How many hours are there from
(a) 9.00 a.m. to 3.00 p.m.? (b) 4.00 a.m. to 1.00 p.m.?
(c) 10.00 a.m. to 4.00 p.m.? (d) 3.00 a.m. to 3.00 p.m.?
(e) 6.00 a.m. to 4.00 p.m.?
2. Calculate how many hours until noon for the following times.
(a) 4.00 a.m. (b) 8.00 a.m. (c) 6.00 a.m.
(d) 11.00 p.m. (e) 7.00 a.m.
3. I woke up at 3.00 a.m. and two hours later the cock crowed. What
time did the cock crow? Discuss.
4. Change into days.
(a) 168 hours (b) 480 hours (c) 720 hours (d) 285 hours
5. Change into hours. Explain the steps followed.
(a) 5 days (b) 12 days (c) 180 min (d) 1 440 min
(e) 3 600 s (f) 7 200 s (g) 360 min
6. Change into hours and minutes. Explain the steps followed.
(a) 206 minutes (b) 156 minutes (c) 236 minutes
7. Change into minutes.
(a) 15 hours (b) 6 hours (c) 10 hours (d) 15 hours
8. Change into seconds.
(a) 2 min (b) 56 min (c) 6 h (d) 3 h
9. A farmer worked for four hours in the morning on Saturday. In the
afternoon she worked for three hours. Find the total time the farmer
worked on Saturday. Discuss and present your answer.
10. A competence mathematics activity started at 8.40 a.m. It ended at9.55 a.m. Find the duration of the activity.
Word list
Units of time Seconds Minutes Hours
Days Duration Time interval
Length of time Starting time Ending time
Task
Do the following.
(i) Read each word aloud to your friend.
(ii) Write the meaning of each of the words above. Discuss with your friend.(iii) Write sentences using each of the words above. Read with your friend.