That’s what I’m say. Sure they can get an approximation, but is that useful enough to do anything?
You send someone a measured 2 leagues away with something that can be seen and heard over that distance. You now know that it takes 4 heartbeats or 2 breaths or something like that for the sound to travel that far.
You now send someone an unknown distance away, and have them do the same thing, how accurate could you estimate that distance?
Yes, there were no timers in the ancient world that could indicate seconds, never mind fractions of a second.
The first clocks that had second hands were built in the 15th century.
IIRC, Archimedes did the experiment between two hills, and got a reasonably accurate figure for sound, but for light, couldn’t conclude anything more than “too fast for me to measure”.
Accurate enough for any application at the time. Which was probably none. At some point bullets were faster than the speed of sound which helped work out the details. An accurate measurement was interesting to early scientists, but still didn’t have any practical application.
The ironic thing about the term “soundings” is that modern-day ships indeed DO use echo equipment of that sort to measure the distance to the seafloor. [Said etymology was news to me tho I did now that they traditionally used weighted lines]
I’d like to see a cite for that.
How do you think he measured the speed (distance per second), when a reliable way of measuring small intervals of time didn’t exist?
Galileo was the first to try to measure the speed of light. He employed a technique that had been used successfully to measure the speed of sound. Having stationed an assistant on a distant hill, he quickly lifted a cover from a lantern. His assistant quickly responded by lifting a cover from his lantern. Galileo then tried to measure the time that elapsed between his uncovering his lantern and his seeing the light from his assistant’s lantern. He did this with several different assistants and over various distances. Galileo correctly concluded that the speed of light was so fast that he was really measuring the reaction time of his assistants rather than the speed of light.
Correct technique though the person was not identified.
Um… there’s a difference between Archimedes and Galileo… and also a difference between the measurement of the speed of sound, and the measurement of the speed of light! 
Aha, that’s where I’ve got you! The ancients didn’t play baseball!
Related question: Was the sonic boom that is created by aircraft breaking the speed of sound something that was known would happen when it first occurred? Theorized about? A surprise?
Ernst Mach first described supersonic waves in 1887. It was previously observed in the use of firearms.
And of course, the Mach unit to describe multiples of the speed of sound is named for him.
Supersonic bullets created a mystery, an extra sound that seemed to occur when the bullet passed by some lucky fellow instead of hitting him. The sound was heard before the sound of the gun firing was heard. It was well known that sound had a speed, so the delay between a bullet hitting or missing something and hearing the sound of it firing was expected. This extra sound turned out to be the sound of the shock wave of the bullet.
And I also gather that there’s a bay somewhere called Music Bay, the measurements of which have us the Sound of Music?
I’ve often wondered: When did anyone first suspect that light had any finite speed? What first led anyone to suppose that light propagation was not instant, and when?
It’s probably the Galileo story that I was (mis)remembering.
Timing, however, isn’t a problem. You can use your pulse, or a segment of a song that you sing at a consistent tempo. Not as precise as a Swiss chronometer or a quartz oscillator, but easily good enough for order-of-magnitude figures.
I don’t know if it was suspected earlier, but the speed was first estimated by using the difference in the timing of the orbits of the moons of Jupiter depending on how far the Earth was away from Jupiter at the time. Rømer's determination of the speed of light - Wikipedia
I wouldn’t call the guttural din one hears at Leonard’s of Great Neck “music” : D
You could use your pulse as a standard even if you’d never heard of Mississippi.
It’s difficult for us today to imagine not having the concepts and tools that we take for granted.
In the ancient world, variable length hours were the norm. There were 12 hours from sunrise to sunset and 12 hours from sunset to sunrise, the length of an hour varying with the seasons.
Sundials showed hours and fractions of an hour, so did astrolabes. Water clocks with a dial only had an hour hand, and needed to be adjusted to run slower or faster as the days lengthened or shortened (and as the temperature changed).
Devices to time the length of speeches, etc. were arbitrary, and varied from one instance to another. The exact length of time didn’t matter, as long as it was the same for everyone.
To determine time accurately to 1/60th of an hour, a minute, was difficult. Seconds, or 1/3,600th of an hour were unknown, and not used.
I suppose you could have counted the number of your pulse beats in an equal-length hour at the equinox, but that wouldn’t have helped, because pulse rates vary so much, even in the same person.
The very concept of quantitative measurement of speed did not exist. You could roughly compare the speed of two things, that was all.
Only with the invention of mechanical clocks in late medieval times did more accurate timekeeping become possible. Later, pendulum-driven clocks made it possible to measure time accurately to the second, and therefore created the possibility of meaningful measurement of speed.