I'm not sure what the 24 Km / sec has to do with it. . . . the Earth is orbiting the Sun at that speed, if not even greater.
Circumference (of a circle) = 2 X Pi X D. So if the earth has a circular orbit around the sun (it doesn't, but it's pretty close) then the equation above implies that the earth travels 2 X 3.1415 X 93,000,000 miles in a one year orbit of the sun.
Which is 584,336,233 miles
Divide that number by 365 (days) and then each DAY the earth travels 1,600,921 miles.
Divide again by 24 this time - each HOUR the earth travels 66,705 miles. (Can you feel the speed? Just sitting "still" at your computer and reading this post, you're traveling 66,705 MPH !!)
Divide by 60 - you and the earth are travelling 1,111 miles per MINUTE.
One last time - divide by 60 again - brings us to 18.5 miles per SECOND.
That is MORE than 24 Km / second. And you have taken this ride at 18.5 miles per second since you were born.
Anyone know how fast the sun is traveling around the circumference of the galaxy?
Anyone know how fast our galaxy is falling toward Andromeda?
Anyone know how fast our Local Group if galaxies is falling towards the Great Attractor?
One thing for sure - we are all moving much, MUCH faster than we think we are.
The Universe Song ... Monty Python... Eric Idle
A handy thing to know for these kinds of calculations is that the approximate number of seconds in one year is π x 107. [This is correct to a relative error of 4 parts per 1000, or about a day and a half.]
So the linear velocity is 9.3 x 107 x 2 x π/(π x 107) mi/s. Cancelling π and 107 this makes your calculation 9.3 x 2 mi/s, which even today's students can do in their heads.