Time - Mathematics Form 1 Notes

• Introduction
  • Units of Time
• The 12 and the 24 hour Systems
• Travel Time Table
• Past KCSE Questions on the topic

Introduction

Units of Time

1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minutes = 60 seconds

Example

How many hours are there in one week?

Solution

1 week = 7 days
1 day =24 hours
1 week = (7x24) hours
= 168 hours

Example

Covert 3h 45 min into minutes
Solution
1 h = 60 min
3 h = (3x60) min
3h 45min =((60x3) + 45) min
=(180+45) min
=225 min

Example

Express 4h 15 min in sec

Solution
1 hour = 60 min
1 min= 60 sec
4h 15 min=(4x60+15) min
=240 + 15 min
=255 min
=255 x 60 sec
=15300 sec.

The 12 and the 24 hour Systems

• In the 12 hour system, time is counted from midnight. The time from midnight to midday is written as am. while that from midday to midnight is written as pm.
• In the 24 hour system, time is counted from midnight and expressed in hours.

Travel Time Table

• Travel timetables shows the expected arrival and departure time for vehicles. Ships, aeroplanes, trains.

Example

1. The table below shows a timetable for a public service vehicle plying between two towns A and D via towns B and C.
   

   Town	Arrival time	Departure time
   A  B  C  D	10.40 P.M 2.30 P.M 4.00 P.M	8.20 A.M 11.00 A.M 2.50 P.M

   1. What time does the vehicle leave town A?
   2. At what time does it arrive in town D?
   3. How long does it take to travel from town A to D.
   4. What time does the vehicle takes to travel from town C to D?

Solution

1. 8.20 A.M
2. 4.00 P.M
3. Arrival time in town D was 4.00 p.m. it departure from town A was 8.20 a.m.
   Time taken= (12.00 − 8.20 + 4h)
   =3 h 40 min +4 h
   = 7h 40 min
4. The vehicle arrived in town D at 4.00 p.m. it departed from town C at 2.50 p.m.
   Time taken = 4.00 − 2.50
   =1h 10 min

Past KCSE Questions on the Topic

1. A van travelled from Kitale to Kisumu a distance of 160km. The average speed of the van for the first 100km was 40km/h and the remaining part of the journey its average speed was 30km/h. Calculate the average speed for the whole journey. (3mks)
2. A watch which looses a half-minute every hour was set to read the correct time at 0545h on Monday. Determine the time, in the 12 hour system, the watch will show on the following Friday at 1945h.
3. The timetable below shows the departure and arrival time for a bus plying between two towns M and R, 300km apart
   

   Town	Arrival	Departure
   M		0830h
   N	1000h	1020h
   P	1310h	1340h
   Q	1510h	1520h
   R	1600h

   1. How long does the bus take to travel from town M to R?
   2. What is the average speed for the whole journey?