Distance in centimeters = Time / 58
Distance in inches = Time / 148
Clearly there is an approximation going on here i.e. 148/58 = 2.5517cm/inch and we know from school that there are exactly 2.54cm to the inch.
OK, if the speed is 340 m/sec that's 34,000 cm per second or 0.034 cm per microsecond but, it's the return journey that is measured in microseconds so the result needs to be divided by 2 and therefore 0.017cm is the distance that the object is away when the echo is received in 1 microsecond and the reciprocal of 0.017 is 58.823. (close to 58)
Maybe they are using 344.8 m/s as speed of sound?
Distance = time * 17000 (in cm)
This one makes no sense until you re-arrange things: - \$\dfrac{distance}{time} = speed = 170m/sec\$
And this is the half the speed of sound.