Does t equals ds or t equals d divided by s?

Answer 1

If t is for time, d is for distance and s is for speed, then the second version in the question is correct: t = d/s .

If you forget, here is a way to work it out. Speed always has units of distance divided by time, as in "miles per hour", or "meters per second", so the units obey

the equation: speed units equals distance units divided by time units,

or s = d / t , in italics to show the letters refer to units, like "a mile" or "a second".

To convert the units equation to the t = d/s form using algebra rules, multiply both

sides of s = d / t by t, leaving st = dt / t , but t/t = 1, hence st = d1 , st=d, because 1 times any number just leaves that same number: 1x5=5, and 1 x leventyleven = leventyleven , if leventyleven is a number in a number system

for which 1 is a unit. Cancellation is not something trivial. It is worthwhile to

explain why it works. Finally, st = d becomes t = d/s by division by s and cancellation, on the left side this time.