Time

An SAT Math micro-topic under Linear relationship word problems (Algebra). Free to read — no account needed.

Time uses a chain of units.
6060 seconds =1= 1 minute, 6060 minutes =1= 1 hour, and 2424 hours =1= 1 day.
Because the steps are fixed, you can convert between them by multiplying or dividing.
To change a larger unit into a smaller one, multiply.
For example, 22 hours =2×60=120= 2 \times 60 = 120 minutes.
To go the other way, divide: 150150 minutes =150÷60=2= 150 \div 60 = 2 hours 3030 minutes.
To find elapsed time, count from the start time to the end time in steps.
From 9:509:50 to 1:201:20, first go to 10:0010:00 (that is 1010 minutes), then to 1:001:00 (that is 33 hours), then to 1:201:20 (that is 2020 minutes).
Altogether that is 33 hours 3030 minutes.
time_timeline.png
Time also appears in rate problems, where distance=speed×time\text{distance} = \text{speed} \times \text{time}.
Rearranged, time=distancespeed\text{time} = \frac{\text{distance}}{\text{speed}}.
So a trip of 150150 miles at 5050 miles per hour takes 15050=3\frac{150}{50} = 3 hours.

Worked examples

How many minutes are in 22 hours 4545 minutes?
Convert the hours to minutes: 2×60=1202 \times 60 = 120 minutes.
Add the extra 4545 minutes: 120+45=165120 + 45 = 165 minutes.
A movie starts at 7:407:40 PM and ends at 9:259:25 PM. How long is it?
From 7:407:40 to 9:409:40 is 22 hours.
But it actually ends at 9:259:25, which is 1515 minutes before 9:409:40.
So the movie runs 11 hour 4545 minutes.
A cyclist rides 3636 miles at a steady speed of 1212 miles per hour. How long does the ride take?
Time is distance divided by speed.
So it takes 3612=3\frac{36}{12} = 3 hours.

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