Time, Duration and Crossing Midnight

Twenty-four hour time removes the ambiguity of a.m. and p.m. Before midday the two systems agree, and after midday you add twelve to the hour, so ten to two in the afternoon is thirteen fifty, and twenty past eleven at night is twenty-three twenty. Midnight is double nought double nought, and it belongs to the new day rather than the old one. Convert everything to twenty-four hour notation before you start, because mixed notation is what causes the errors. And if you see a time written as twenty-three twenty p.m., that is already twenty-four hour and the p.m. is redundant — read the number, not the label.

To find how long something lasted, hop. From twenty-five past two in the afternoon, hop to the next whole hour — that is twenty-five minutes to three o'clock. Then hop in whole hours to five o'clock, which is two hours. Then the leftover ten minutes. Add the hops: two hours thirty-five. Trying to subtract the clock times as though they were ordinary numbers gives two point seven five, which means nothing at all. Hopping never requires borrowing, which makes it both faster and safer when you are working quickly.

When an event runs past midnight, split it at midnight and add the two pieces. From twenty past eleven at night to midnight is forty minutes. From midnight to ten to two is one hour fifty. Together that is two hours thirty, or a hundred and fifty minutes. If you try to subtract directly you get a negative number, and that negative is useful — it is the signal that the clock has passed midnight and you need to split. Whenever the finishing time looks smaller than the starting time, that is what has happened.

Adding a duration works the same way in reverse: whole hours first, then the minutes. Twenty to eight in the evening plus three hours is twenty to eleven. Then forty minutes plus forty-five minutes is eighty-five minutes, which is one hour and twenty-five, so the finish is twenty-five past eleven. The only real difficulty is that you carry at sixty rather than at a hundred, so when the minutes go past sixty you carry one hour and keep the remainder. Saying sixty out loud as you carry is a surprisingly effective habit.

The hardest version feeds the duration into a rate. The stream runs from twenty past eleven to ten to two, which we worked out is two and a half hours. At two gigabytes an hour that is five gigabytes. The thing to be careful about is the unit: to multiply by a rate given per hour, the duration has to be in hours, so do the whole duration calculation in minutes where it is safe, and convert to hours at the very last moment. A hundred and fifty minutes is two and a half hours, and two and a half times two is five. Quiz and exercises now.