Exercises: Measurement of time

Look at the following image of a wall clock that uses the Roman numeral system. State the time shown on the clock, expressing the hours and minutes in the decimal system.

In the study of history and time, we use units larger than a year. Complete the following equivalences:

1. a) $3$ centuries = $\dots$ years.
2. b) $5$ decades = $\dots$ years.
3. c) $8$ lustrums = $\dots$ years.
4. d) $200$ years = $\dots$ centuries.

A short video on social media lasts exactly $145$ seconds. Express the duration of this video in compound form, that is, stating the minutes and seconds it lasts ($145$ s = $\dots$ min $\dots$ s).

This afternoon you spent two periods of time studying for the math exam. The first lasted $1$ h $40$ min and the second $55$ min. Calculate the total study time, expressing the result in hours and minutes.

An animated film starts at $17:15$ and ends at $18:50$. What is the exact duration of the film in hours and minutes?

An elite athlete completed a marathon in an official time of $2$ hours, $12$ minutes and $15$ seconds.

1. a) Express the total duration of the race in seconds only.
2. b) If their coach tells them to reduce their time by $450$ seconds for the next competition, what would their new target time be, expressed in compound form ($h$, $min$, $s$)?

The high-speed train leaves Mexico City at $08:45:00$ and is scheduled to arrive in Guadalajara at $11:17:25$. Due to a minor technical delay, the train arrived at $11:23:10$.

1. a) What was the scheduled duration of the trip?
2. b) How much delay did the train experience compared to the scheduled time?

A youth association organises a park clean-up day that lasts a total of $5$ hours, $42$ minutes and $36$ seconds. If $4$ work teams have been formed and they want to split the total time equally so that each team covers a different time slot without overlapping:

How long should each team's shift last? (Carry out the division in the sexagesimal system).

An ultra-trail runner has completed a $105 \text{ km}$ race in a time of $14 \text{ h } 18 \text{ min } 36 \text{ s}$.

1. a) Calculate their average speed in meters per second ($m/s$), rounding to hundredths.
2. b) If the course record is $12 \text{ h } 45 \text{ min } 50 \text{ s}$, by how many seconds per kilometer would they have needed to reduce their time to match the record?

An analogue clock shows exactly $10:15:30$ (10 hours, 15 minutes and 30 seconds). Calculate the exact angle formed by the hour hand and the minute hand at that precise moment. Note: Take into account that the hour hand moves continuously as the minutes and seconds pass.

The planet Mars has a rotation period (a "sol") of approximately $24 \text{ h } 37 \text{ min } 22 \text{ s}$. An astronaut arrives on Mars and starts an Earth stopwatch and a stopwatch set to Martian time right at sunrise. What Earth time difference will there be between both clocks when exactly one Martian week (7 sols) has elapsed? Express the result in compound form (hours, minutes and seconds).

An internet server processes user requests. It is known to take an average of $1.25$ hundredths of a second to handle each request. If during a cyberattack the server receives a total of $2^{18}$ requests:

1. a) Calculate the total number of requests in the decimal system.
2. b) Calculate the total time it will take for the server to process them all. Express the final result in hours, minutes and seconds.