0580 · 1.15Time

Time units and conversions

0:00A flight can arrive at a local time that seems inconsistent with its journey length. A train journey can finish after midnight, when the clock shows a smaller number than at departure. Neither situation means time has gone backwards. By the end of this video, you will understand how clocks, durations and time zones fit together. The key distinction is between a time of day and a duration. A time of day identifies a particular moment, such as ten in the morning.

0:25A duration measures how long something lasts, such as twenty minutes. Calculating with time means keeping these two ideas separate and choosing suitable units. One minute contains sixty seconds, and one hour contains sixty minutes. A day contains twenty-four hours, while a week contains seven days. Converting to a smaller unit makes the number larger, because more of the smaller pieces are needed. Converting to larger units means dividing by the number contained in each larger unit.

0:52For example, three hours contains three groups of sixty minutes, giving one hundred and eighty minutes. To convert that duration into seconds, multiply one hundred and eighty by sixty. The result is ten thousand eight hundred seconds. The duration stays unchanged even though its numerical value changes. Calculate two hours, eighteen minutes and forty-five seconds in seconds. First, 2 × 60 gives one hundred and twenty minutes. Adding eighteen gives one hundred and thirty-eight minutes.

1:22Multiplying that total by sixty gives eight thousand two hundred and eighty seconds. Finally, adding forty-five gives eight thousand three hundred and twenty-five seconds. Months need extra care because they do not all contain the same number of days. There are twelve months in a year, but a month is not exactly four weeks. For the year conversion used in this topic, take one year as three hundred and sixty-five days.

1:46If specific calendar dates are given, use the actual month lengths. April, June, September and November have thirty days, while the other months except February have thirty-one. February has twenty-eight days, or twenty-nine in a leap year. Two years and three months therefore equals twenty-seven months. Three weeks and four days is twenty-one days plus four, which makes twenty-five days.

Clock notation and time formats

2:09Clock notation is not decimal notation. Two hours and thirty minutes is two and a half hours because thirty is half of sixty. It is not two point three hours. To interpret decimal hours correctly, multiply the decimal part by sixty to find the minutes. Consider a duration of two point four hours. The whole number part gives two hours. Multiplying zero point four by sixty gives twenty-four minutes. Therefore, the duration is two hours and twenty-four minutes, not two hours and forty minutes.

2:37On an analogue clock, the long minute hand completes one full turn every hour. The sixty minute marks are arranged around twelve numbered positions, so each numbered step represents five minutes. A minute hand pointing at three therefore shows fifteen minutes past the hour. The short hour hand moves gradually, so it should sit slightly beyond seven. This clock shows seven fifteen, but the hands alone do not identify morning or evening.

3:02If a second hand is shown, each small mark represents one second. For the twelve-hour clock, the morning label applies from midnight until just before noon. The afternoon label applies from noon until just before midnight. The twenty-four-hour clock counts hours from midnight, which is written as zero zero hours and zero zero minutes. Three fifteen in the morning is written with zero three for the hours and fifteen for the minutes.

3:26Three fifteen in the afternoon becomes fifteen fifteen. The minutes stay the same because only the hour numbering changes. For afternoon and evening hours from one to eleven, add twelve to obtain the twenty-four-hour hour number. To convert seventeen twenty back, subtract twelve from seventeen to get five twenty in the afternoon. Twelve noon is written as twelve hundred, while twelve midnight becomes zero zero zero zero. These boundary cases prevent the mistaken rule of always adding or subtracting twelve.

Calculating elapsed time and timetables

3:55When adding durations, sixty minutes must be exchanged for one hour. For example, one hour fifty minutes plus two hours twenty-five minutes gives three hours seventy-five minutes before regrouping. Seventy-five minutes contains one hour and fifteen minutes. The final duration is therefore four hours and fifteen minutes. For subtraction, calculate five minutes twelve seconds minus two minutes forty-seven seconds. Exchange one minute for sixty seconds, giving four minutes seventy-two seconds.

4:23Subtracting forty-seven from seventy-two leaves twenty-five seconds. Then 4 − 2 gives two minutes. The answer is two minutes and twenty-five seconds. Elapsed time means the duration between a starting time and a finishing time. Counting forwards through convenient clock times often makes this easier than subtraction. From ten forty-five to eleven hundred is fifteen minutes, then reaching noon takes sixty minutes. Another twenty minutes reaches twelve twenty, giving ninety-five minutes altogether.

4:52A timetable gives clock times rather than journey durations. Read the station names and service headings before doing any calculation. In this example, a passenger leaves Central at twenty-three forty-eight on Tuesday and reaches Junction at zero thirty-five on Wednesday. The connecting train departs at one zero five and reaches Coast at two twenty. Calculate the first journey by splitting it at midnight. From twenty-three forty-eight to midnight takes twelve minutes.

5:18From midnight to zero thirty-five takes another thirty-five minutes. Adding twelve and thirty-five gives a journey duration of forty-seven minutes. The wait runs from zero thirty-five until one zero five. Reaching one o’clock takes twenty-five minutes, and another five minutes gives a waiting time of thirty minutes. The second train takes sixty minutes to reach two zero five. Adding the remaining fifteen minutes gives seventy-five minutes for that journey. The total elapsed time includes both journeys and the wait.

5:4647 + 30 gives seventy-seven minutes. Adding seventy-five produces one hundred and fifty-two minutes. Two hours accounts for one hundred and twenty minutes, leaving thirty-two. The complete trip therefore takes two hours and thirty-two minutes.

Time zones and exam checks

6:01Time zones mean that different places can display different clock times at the same instant. If City B is three hours thirty minutes ahead of City A, its clock shows a later time. Add that difference when converting from City A to City B. Subtract it when converting in the opposite direction. An exam-style flight leaves City A at twenty-two forty on Tuesday and lasts seven hours fifty minutes. Adding seven hours gives five forty on Wednesday in City A time.

6:28Another fifty minutes brings this to six thirty. This is the arrival instant expressed using the departure city’s clock. City B is three hours thirty minutes ahead of City A. Adding three hours to six thirty gives nine thirty on Wednesday. Adding thirty minutes gives a local arrival time of ten hundred hours on Wednesday. Keep the journey duration and the time-zone adjustment separate because they describe different things. Typical mistakes include treating minutes as hundredths, ignoring midnight, and choosing the wrong time-zone direction.

6:59A duration of one hour thirty minutes is one point five hours, not one point three hours. When a journey crosses midnight, include the change of day. For time zones, ask which clock should show the later reading at the same instant. These methods must work without a calculator on Paper Two, while Paper Four allows a calculator. Show your conversions and intermediate times clearly on either paper. Exact time answers should remain exact unless the question requests rounding.

7:24The usual three significant figure convention does not mean rounding an exact clock time or duration. The central idea is that clocks locate moments, while durations measure the gaps between them. Convert using sixty seconds per minute, sixty minutes per hour and twenty-four hours per day. Read timetables carefully, include waiting time, and track date changes. For time zones, calculate the arrival instant first, then express it using the destination’s clock.