Measuring time
A high-speed AVE train leaves Madrid at $08{:}45{:}00$ and is due to arrive in Seville at $11{:}17{:}25$, but it arrives at $11{:}23{:}10$. How long was the journey scheduled to take, and how late has the train been? To solve this you need to handle clock times well, and also the larger units of time that we use when we talk about history.
Units of time longer than a year
In the study of history and time, we use units larger than a year. Complete the following equivalences: a) $3$ centuries = $\dots$ years. b) $5$ decades = $\dots$ years.…
In the study of history and time, we use units larger than a year. Complete the following equivalences:
- a) $3$ centuries = $\dots$ years.
- b) $5$ decades = $\dots$ years.
- c) $8$ lustrums = $\dots$ years.
- d) $200$ years = $\dots$ centuries.
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…
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).
Calculating a duration from the start and end times
To find out how long something lasts when it starts at one time and ends at another, you subtract the times in compound form, "borrowing" in sixties when necessary.
The high-speed train (AVE) leaves Madrid at $08:45:00$ and is scheduled to arrive in Seville at $11:17:25$. Due to a minor technical delay, the train arrived at…
The high-speed train (AVE) leaves Madrid at $08:45:00$ and is scheduled to arrive in Seville at $11:17:25$. Due to a minor technical delay, the train arrived at $11:23:10$.
- a) What was the scheduled duration of the trip?
- b) How much delay did the train experience compared to the scheduled time?
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 animated film starts at $17:15$ and ends at $18:50$. What is the exact duration of the film in hours and minutes?
Sharing out time and speeds with hours, minutes and seconds
Sharing a total time between several turns, or calculating an average speed, requires you to convert everything into the same unit first (almost always seconds or a single decimal unit).
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…
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 $14 \text{ h } 18 \text{ min } 36 \text{ s}$. a) Calculate their average speed in metres per…
An ultra-trail runner has completed a $105 \text{ km}$ race in a time of $14 \text{ h } 18 \text{ min } 36 \text{ s}$.
- a) Calculate their average speed in metres per second ($m/s$), rounding to hundredths.
- b) If the course record is $12 \text{ h } 45 \text{ min } 50 \text{ s}$, by how many seconds per kilometre would they have needed to reduce their time to match the record?
The angle between the hands of a clock
The hands of a clock also move in the sexagesimal system: the minute hand covers $360°$ in $60$ min, and the hour hand covers $360°$ in $12$ h, also moving a little with every minute that passes.
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.
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.
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…
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.