Time

Syllabus tag: KCSE | Mathematics | Form 1 | Topic 16 Time

Lesson objectives

By the end of this topic, you should be able to:

• State the units of time and convert from one to another.
• Relate the 12-hour and 24-hour clock systems.
• Read and interpret travel timetables.
• Solve problems involving travel time.

Time

Time is measured in seconds, minutes and hours. Unlike other units, it does not work in tens.

a) Units

60 seconds make a minute. 60 minutes make an hour. 24 hours make a day.

7 days make a week. 365 days make a year, or 366 in a leap year.

The sixties are what catch people out. Two and a half hours is 2 h 30 min, not 2.5 written as 2 h 50 min.

b) Converting

Hours to minutes: multiply by 60. Minutes to seconds: multiply by 60.

Going the other way, divide by 60.

To convert 3.25 hours into hours and minutes, take 0.25 × 60 = 15. So it is 3 h 15 min.

To convert 2 h 45 min into hours as a decimal, take 45 ÷ 60 = 0.75. So it is 2.75 hours.

Speed calculations need the decimal form. Timetables need hours and minutes. Know which the question wants.

c) The 12-hour and 24-hour systems

The 12-hour system needs a.m. or p.m. to be unambiguous.

The 24-hour system counts from 0000 to 2359 and needs neither.

For afternoon and evening times, add 12 to the hours. So 3.45 p.m. becomes 1545 h.

Always write four digits. Nine in the morning is 0900 h.

Midnight is 0000 h and noon is 1200 h. These two are the ones most often reversed.

d) Reading timetables

Travel timetables use the 24-hour clock, which removes any ambiguity.

Read down a column for one journey. Read across a row for one stop.

e) Journey time

Subtract the departure time from the arrival time.

If the minutes will not subtract, borrow one hour and add 60 minutes.

Borrowing 100 instead of 60 is the standard error here.

f) Journeys past midnight

If a journey crosses midnight, add 24 hours to the arrival time before subtracting.

A bus leaving at 2130 h and arriving at 0215 h arrives at 2615 h in this working. Then 2615 − 2130 = 4 h 45 min.

g) Where this is used

Catching transport. Planning a schedule. Calculating speed, where time must be in decimal hours. Working out pay from hours worked.

Words to know

• a.m. -- the hours from midnight to noon.
• p.m. -- the hours from noon to midnight.
• 24-hour clock -- a four-digit system running 0000 to 2359.
• Average speed -- total distance divided by total time.
• Leap year -- a year of 366 days, divisible by 4 with the century exception.

:::checkpoint Check yourself

1. Write 7.20 p.m. in the 24-hour system.
2. Convert 3 h 24 min into hours as a decimal.
3. A bus leaves at 0940 h and arrives at 1315 h. How long is the journey?
4. Why must you borrow 60 rather than 100 when subtracting times? :::

Bridge to practice

The exercises begin with units and the base-60 conversions, move through clock systems and timetables, and finish with speed, distance and average speed. Before any speed calculation, convert every time to decimal hours and check that the distance unit matches.