Duration across Midnight and across Days

A duration is the distance between two times, and the safe way to measure it is to hop through landmarks, exactly as bridging did for subtraction. From three forty to five ten: twenty minutes reach four o'clock, an hour reaches five, ten more minutes reach five ten. One hour thirty. Subtracting the times like ordinary numbers gives one point seven, which is nonsense, because an hour has sixty minutes, not a hundred. Hop, then add the hops.

When the interval crosses midnight, midnight is simply the biggest landmark. From nine fifty at night to six thirty in the morning: two hours ten minutes reach midnight, then six hours thirty from midnight, eight hours forty altogether. Eleven forty at night to two forty-five in the morning: twenty minutes to midnight, then two hours forty-five, three hours five. Stop at twelve, write down what you have, carry on.

The twenty-four-hour clock counts straight through the day, from zero-zero-zero-zero at midnight to twenty-three fifty-nine. To turn a pm time into it, add twelve to the hour; to turn it back, take twelve off. Eighteen fifty plus a quarter of an hour: ten minutes reach nineteen hundred, five more reach nineteen oh five, which is five past seven in the evening. Durations are easier in twenty-four-hour time because nothing restarts at twelve — but the minutes still roll over at sixty, so eighteen fifty plus fifteen is nineteen oh five, never eighteen sixty-five.

A journey longer than a day is handled in whole days first. Fifty hours is two days and two hours: take off twenty-four for each day and keep what is left. Whole days move the day name and leave the clock alone; then the extra hours move the clock and perhaps the day once more. Leave Saturday at twenty-two hundred and travel thirty hours: one day later is Sunday twenty-two hundred, six hours more is Monday oh four hundred. A twenty-hour flight from Friday thirteen hundred: eleven hours reach Saturday midnight, nine more reach Saturday oh nine hundred. Say the day at every step.

When the finish is known and the start is wanted, hop backwards. A movie ends at four fifteen after running one hour fifty: fifteen minutes back reaches four, an hour back reaches three, and the remaining thirty-five minutes reach two twenty-five. When the duration comes in pieces — a forty-minute route, a fifteen-minute break, a twenty-five-minute route — add them first, eighty minutes, then hop back once. Check by running forwards from the start. Quiz and exercises now.