Mathematics Form 1-4 : CHAPTER TEN – TIME

Specific Objectives

By the end of the topic the learner should be able to:

1. Convert units of time from one form to another
2. Relate the 12 hour and 24 hour clock systems
3. Read and interpret travel time-tables
4. Solve problems involving travel time tables.

Content

1. Units of time
2. 12 hour and 24 hour clock systems
3. Travel time-tables
4. Problems involving travel time tables

Introduction

Units of time

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Example

How many hours are there in one week?

Solution

1 week = 7 days

1 day = 24 hours

1 week = (7 × 24) hours

= 168 hours

Example

Convert 3h 45 min into minutes

Solution

1 h = 60 min

3 h = (3 × 60) min

3h 45min = ((60 × 3) + 45) min

= (180 + 45) min

= 225 min

Example

Express 4h 15 min in seconds

Solution

1 hour = 60 min

1 min = 60 sec

4h 15 min = (4 × 60 + 15) min

= 240 + 15 min

= 255 min

= 255 × 60 sec

= 15,300 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 show the expected arrival and departure times for vehicles, ships, aeroplanes, and trains.

Example

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

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 take 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. Its departure from town A was 8.20 a.m.

   Time taken = (12:00 – 8:20 + 4 h)

   = 3 h 40 min + 4 h

   = 7 h 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

   = 1 h 10 min

End of topic

Past KCSE Questions on the topic

1.) A van travelled from Kitale to Kisumu, a distance of 160 km. The average speed of the van for the first 100 km was 40 km/h and for the remaining part of the journey its average speed was 30 km/h. Calculate the average speed for the whole journey. (3 mks)

2.) A watch which loses half a minute every hour was set to read the correct time at 05:45 on Monday. Determine the time, in the 12 hour system, the watch will show on the following Friday at 19:45.

3.) The timetable below shows the departure and arrival time for a bus plying between two towns M and R, 300 km apart.

(a) How long does the bus take to travel from town M to R?

(b) What is the average speed for the whole journey?