mozaMedical by Mozaik Education

Time

In the very beginning, the measurement of time was linked to nature. Months, parts of the day, and activities such as sowing and harvesting were linked to the movement of the sun or moon. The Egyptians divided the day into \latex{ 24 } equal parts. They used water clocks to tell how much of the day had passed. The Greeks and Chinese constructed sundials, using the shadow of a rod to measure the passage of time. As technology developed, timekeeping devices became more and more accurate.

Hi Steve! The train leaves at \latex{ 14:15 }.
The journey takes \latex{ 1 } \latex{hour} \latex{and} \latex{ 20 } \latex{minutes},
so I’ll be there at half past three.

Time: when an event happens (the train leaves at \latex{ 14:15 }).
Duration: how long an event takes (the journey takes \latex{ 1 } \latex{ hour } \latex{ and } \latex{ 20 } \latex{ minutes }).

The units of time:

\latex{1 \;\textcolor{#ff0000}{second}}

\latex{1 \;\textcolor{#ff0000}{minute}}

\latex{1 \;\textcolor{#ff0000}{hour}}

\latex{1 \;\textcolor{#ff0000}{day}}

\latex{1 \;\textcolor{#ff0000}{week}}

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\latex{\times\;60}

\latex{\times\;24}

\latex{\times\;7}

\latex{1\;{ hour}\;\; =\;\; 60\;{ minutes}\;\;=\;\; 3,600 \;{ seconds}}

\latex{1\;{ day} = 24\;{ hours}\qquad 1 \;{ week} = 7\;{ days}\qquad 1\;{ year} = 12\;{ months}}

\latex{ 1 } \latex{ month } \latex{ = } \latex{ 28 } \latex{ (29) }, \latex{ 30 } or \latex{ 31 } \latex{ days }

\latex{ 1 } \latex{ year } ≈ \latex{ 52 } \latex{ weeks }
\latex{ 1 } \latex{ year }\latex{ = } \latex{ 365 } \latex{ (366) } \latex{ days }

In leap years, February is \latex{ 29 } \latex{ days } long, which makes a leap year \latex{ 366 } \latex{ days } long .

Which year is a leap year? If the year can be divided by \latex{ 4 } but not by \latex{ 100 } (unless it can be divided by \latex{ 400 }), then it is a leap year. For example, \latex{ 1900 } was not a leap year, but \latex{ 2000 } was.

Exercises

{{exercise_number}}. Ant measures time in \latex{ seconds }, Mouse in \latex{ minutes }, Rabbit in \latex{ hours } and Elephant in \latex{ days }. Convert the following durations into the units they use.

a) \latex{ 45 } \latex{ minutes }
b) \latex{ 2 } \latex{ hours } \latex{ 20 } \latex{ minutes }
c) \latex{ 1 } \latex{ day }

a) \latex{ 1 } \latex{ day }
b) \latex{ 6,600 } \latex{ s }
c) \latex{ 4 } \latex{ years }

a) \latex{ 5,400 } \latex{ minutes }
b) \latex{ 4 } \latex{ years }

c) \latex{ 100 } \latex{ years }

a) \latex{ 1 } \latex{ leap } \latex{ year }
b) \latex{ 4 } \latex{ years }
c) \latex{ 744 } \latex{ hours }

{{exercise_number}}. The time zone difference between New York and Paris is \latex{ 4 } \latex{ hours }. If it is \latex{ 10 } in the morning in New York, it is \latex{ 2 } in the afternoon in Paris. What might a student in New York be doing while a student in Paris is

a) getting up;

b) eating dinner;

c) leaving school?

{{exercise_number}}. Which one is the longer duration?

a) \latex{ 40 } \latex{ days } or \latex{ 1,000 } \latex{ hours }

b) \latex{ 32,700 } \latex{ minutes } or \latex{ 50 } \latex{ hours }

c) \latex{ 24,000 } \latex{ minutes } or \latex{ 21 } \latex{ days }

d) \latex{ 80 } \latex{ days } or \latex{ 6 } \latex{ million } \latex{ seconds }

e) \latex{ 11 } \latex{ year } or \latex{ 5 } \latex{ million } \latex{ minutes }

f) quarter of an \latex{ hour } or \latex{ 1,000 } \latex{ s }

{{exercise_number}}. Which of the three durations is most likely to be true for each?

a) A play at a theatre: \latex{ 120 } \latex{ minutes }; \latex{ 1,200 } \latex{ seconds }; \latex{ 12 } \latex{ hours }.
b) A tennis match: \latex{ 1,500 } \latex{ seconds; } \latex{ 15 } \latex{ minutes }; an \latex{ hour } and a half.
c) A single heartbeat: \latex{ 1 } \latex{ minute }; \latex{ 1 } \latex{ second }; one-tenth of an \latex{ hour }.
d) The train journey from London to Manchester: \latex{ 132 } \latex{ minutes }; \latex{ 22 } \latex{ hours }; \latex{ 400 } \latex{ seconds }.

{{exercise_number}}. The brand-new music record from The Raspberries features the following tracks:

1. On the road: \latex{ 2 } \latex{ min } \latex{ 15 } \latex{ s };

2. I'm back: \latex{ 3 } \latex{ min } \latex{ 5 } \latex{ s };

3. The dreamer: \latex{ 2 } \latex{ min } \latex{ 45 } \latex{ s };

4. Dandelions: \latex{ 1 } \latex{ min } \latex{ 32 } \latex{ s };

5. Cheers to that: \latex{ 4 } \latex{ min } \latex{ 19 } \latex{ s };

6. Wonderfloor: \latex{ 6 } \latex{ min } \latex{ 30 } \latex{ s };

7. Mr. Darkside: \latex{ 3 } \latex{ min } \latex{ 27 } \latex{ s };

8. Shape of two: \latex{ 4 } \latex{ min } \latex{ 52 } \latex{ s; }

9. No fuss: \latex{ 2 } \latex{ min } \latex{ 18 } \latex{ s }.

How many \latex{ minutes } would it take to listen to the whole album in one sitting?

{{exercise_number}}. If it is \latex{ 11 } in the morning now, what time will it be in

a) \latex{ 48 } \latex{ hours };

b) \latex{ 60 } \latex{ hours };

c) \latex{ 100 } \latex{ hours };

d) \latex{ 1,000 } \latex{ hours?}

{{exercise_number}}. If the \latex{ 4 }th of March is a Friday, what day do the following dates fall on in the same year?

a) March \latex{ 25 }th

b) April \latex{ 1 }st

c) May \latex{ 15 }th

{{exercise_number}}. There are four children in a family. The sum of their ages is \latex{ 20 } \latex{ years }. What will the sum of their ages be in \latex{ 3 } \latex{ years ?}

{{exercise_number}}. Approximately how much time passed between the year zero and the year \latex{ 2000 }?

a) \latex{ 1 } \latex{ billion } \latex{ seconds }
b) \latex{ 1 } \latex{ billion } \latex{ minutes }
c) \latex{ 1 } \latex{ billion } \latex{ days }

Quiz

A chemist discovered a chemical reaction that takes \latex{ 80 } \latex{minutes} to carry out while wearing a jacket, but only \latex{ 1 } \latex{hour} \latex{and} \latex{ 20 } \latex{minutes} while not wearing a jacket. How is this possible?

Mathematics 5.

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