# Calculating with Time

See also: NumbersEven otherwise highly numerate people have been known to throw up their hands in horror at the thought of adding together times.

A system like time, which is not decimal, can be counter-intuitive and requires concentration.

However, with a bit of application, you too can learn how to calculate with time, and gain confidence in manipulating hours, minutes and seconds.

### Basic Units of Time

The basic units of time, which allow you to do calculations involving time, are:

Unit | Notes | |

Second | The second is the International System of Units (SI) measurement for time. The symbol 's' is used to denote a second. Seconds are also commonly abbreviated to sec. | |

Minute | 60 Seconds | A minute nearly always has sixty seconds. However, very occasionally (approx. once every 18 months) a minute can have 61 seconds. These 'leap seconds' are used to keep our clocks aligned to the earth's rotation around the sun. |

Hour | 60 Minutes | It is common to talk about 'half an hour' (30 minutes) and 'quarter of an hour' (15 minutes). |

Day | 24 hours | |

Week | 7 days | It is also common for people to talk about a work week, usually 5 days (Monday - Friday) and weekends (Saturday and Sunday). |

Month | 28,29, 30 or 31 days. | Different months have different numbers of days. All months have either 30 or 31 days except for February. February has 28 days in a common year and an extra day in a leap year; the 29^{th}day of February is called the leap day. |

Year | 12 Months | A year always has 12 months. A year has approximately 52 weeks. A common year has 365 days and a leap year (occurring mostly every 4 years) has 366 days. |

Decade | 10 Years | |

Century | 100 Years | |

Millennium | 1,000 Years | |

**Years are commonly split into quarters, especially in business and education settings with** each quarter being three months or approximately 90 days. Quarters in a specific business or sector may not necessarily be the same as those indicated below:

The number of days in a month varies. All months have the same number of days each year except for February which has 28 days in a common year and 29 in a leap year.

Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | |||||||

Month | Days | Month | Days | Month | Days | Month | Days | |||

January | 31 | April | 30 | July | 31 | October | 31 | |||

February | 28/29 | May | 31 | August | 31 | November | 30 | |||

March | 31 | June | 30 | September | 30 | December | 31 |

**As the number of days in a month varies this also means that the number of weeks in a month varies too**.

People often use approximations when calculating the number of days in months. For example, it is common to use the assumption that a month contains four weeks, even though only February in a common year actually does so.

This makes it hard to convert from months to weeks and vice versa, unless you know which months are being used, because there is no immediate ‘conversion factor’.

Top Tip!

If you are converting between months and weeks, the best way to do so is via years, because they always contain 12 months (even in a leap year).

- To convert months to weeks, divide by 12 and multiply by 52.
- To convert weeks to months, divide by 52 and multiply by 12.

The answers you get will be good approximations.

## Writing Time

There are many different ways to write time. The simplest (digital) form is as written hh.mm or hh:mm, for example 10.21 or 10:21.

Hours may be either divided into 24 or two lots of 12, in which case all those before noon are designated __am__ (*ante meridiem*) and those after noon are __pm__ (*post meridiem*). For example 4:10pm is the same time as 16:10.

You can also describe time in words, such as 'ten minutes past/after twelve', or 'ten past twelve'. Up to half way through an hour, we describe ‘minutes past’ the hour; beyond ‘half past’ we talk about minutes to/before the next hour.

Calculations of How Much Time has Passed

You may need to do calculations of how much time has passed, for example, to work out the end time of an examination, how long you will have to wait for a train, or perhaps to calculate race results.

If time is described in words, you will need to convert it into a digital form in order to do any calculations.

It is also simpler to use the 24 hour clock to avoid any confusion, unless all your figures are either am or pm.

### Example time formats:

## Calculating the Passage of Time

In the normal way of things, to calculate how much one thing is greater than another you would simply subtract one from another. However, subtracting time is complicated because it’s not decimal. Instead of the columns being hundreds, tens and units, they are hours, minutes and seconds.

Top Tip

If you have a scientific electronic calculator, you will almost certainly have a button that will calculate time. Technically, it’s for degrees but as there are 60 minutes in a degree, and 60 seconds in a minute, you can also use it to calculate time.

The button will have a symbol like this:

At the very least, you should be able to use that to convert time to decimals and back again, making calculations much easier.

The other way of calculating how much time has passed between Time A and Time B is:

- Work out how many minutes from Time A to the next hour (or minute, if in minutes and seconds).
- Work out how many hours between that next hour, and the last whole hour before Time B.
- Work out how many minutes from the whole hour until time B.
- Add these three numbers together.

### Worked Examples

Pat was due to catch a train at 11.44am, which she has just missed. The next train is not until 1.17pm. How long will she have to wait?

Before you start, convert all the numbers to 24-hour clock for ease. 11.44am becomes 1144 and 1.17pm becomes 1317.

*The number of minutes from 11:44 to 12:00 (the next hour) is 16.**The number of hours from 12:00 to 13:00 is one.**The number of minutes from 13:00 to 13:17 is 17.*

The total time that Pat will have to wait is 1 hour plus (16 + 17) minutes = 1 hour 33 minutes.

I am organising a series of canoe races, and have synchronised clocks for the start and the finish. The plan is for the first race to start at about 30 minutes after synchronisation, then four more races to start at 2-minute intervals after that, but it never works exactly. The starter keeps a record of the exact times, and it turns out that on this occasion, races started at 28:02, 30:00, 32:15, 34:40 and 37:00.

The finish line has a clock, which is exactly synchronised with the start clock, and the finisher records the time on the clock when the racers cross the finish line.

For each of the following finish times, work out how long the competitor took (click on the + icons to see the working and answers):

James started at 28:02 and finished at 59:02. How convenient, there are no additional seconds! You can simply subtract 28 from 59, and discover that he took **31 minutes** exactly.

Simon started at 34:40 and finished at 1:10:34. It’s probably easier to call that (60+10) = 70:34. From 34:40 to 35:00 is 20 seconds. From 35:00 to 70:00 is 35 minutes. From 70:00 to 70:34 is 34 seconds. Simon therefore took 35 minutes plus 34 seconds plus 20 seconds = **35:54 minutes**

Mary started at 30:00 exactly, and finished at 1:15:02, or 75:02. Again, this is quite straightforward. There are no seconds before the next minute, but there are 45 minutes from 30:00 to 75:00, and 2 seconds from 75:00 to 75:02. She therefore took **45:02 minutes**.

### Conclusion

The most important thing when calculating with time is to check whether* the answer looks about right?*

If your two numbers are less than an hour apart, is your answer less than an hour? If they are about 2 hours apart when you look at them, is your answer? If not, you may have lost or gained some time somewhere!

If you want to know more about ‘about right’ take a look at our page on Estimation, Approximation and Rounding.

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Measurement Systems | Probability