we wouldn't have 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day.
Say thank you to the Egyptians who used a Duodecimal (base 12) number system (most likely because each finger has 3 joints). They divided the day into 12 parts and eventually the night into 12 parts thus 24 parts per day-night cycle. Every day and every night were divided this way irrespective of the actual length of time. Thus short winter days and long winter nights still had 12 parts each and long summer days and short summer nights the same 12 divisions each. That these parts "hours" be of equal length each was not considered until the Greeks (Hipparchus) and did not became common until after mechanical clocks were developed in the 14th century.
As for the 60-parts say thank you to the Sumerians who used a Sexagesimal (base 60) system. Why 60 is unknown but it is convenient for expressing fractions, since 60 is the smallest number divisible by the first six counting numbers as well as by 10, 12, 15, 20 and 30.
The Greek astronomer Eratosthenes used this system to divide a circle into 60 parts in order to devise an early geographic system of latitude. A century later, Hipparchus normalized the lines of latitude, making them parallel and obedient to the earth's geometry. He also devised a system of longitude lines that encompassed 360 degrees and that ran north to south, from pole to pole. In his treatise
Almagest, Claudius Ptolemy subdivided each of the 360 degrees of latitude and longitude into smaller segments. Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division,
partes minutae primae, or first minute, became known simply as the "minute." The second segmentation,
partes minutae secundae, or "second minute," became known as the second. Clock faces which were circular eventually followed this plan though not until the 16th century. Initially the hour was simply divided into 12 parts though 1/2, 1/4, and 1/3 were more convenient.
By the by, since the advent of UTC timekeeping, in order to keep atomic time in agreement with astronomical time, leap seconds occasionally must be added to UTC. Thus, not all minutes contain 60 seconds. A few rare minutes, occurring at a rate of about eight per decade, actually contain 61.