Math: how fast does one gear turn, if the other gear turns at so-and-so rpm?

Tutoring math, problems might come up about the turns (rpm) of one gear relative to another. The tutor mentions an example.

Question: Suppose Gear A (14 teeth) and Gear B (21 teeth) are enmeshed. If Gear B turns 60 rpm, how fast does Gear A turn?

Solution: the idea is that the same number of teeth are contacted, for each gear, during a given time. At 60 rpm, in one minute, 60*21=1260 total teeth are contacted for Gear B. Therefore, 1260 teeth must also be contacted for Gear A during that same minute. Gear A’s number of turns for that minute will be 1260/14 = 90 turns. So, Gear A turns at 90 rpm, if Gear B turns at 60 rpm.

Source:

Travers, K.J., Dalton, L.C., Brunner, B.F. and Taylor, A.R. (1977). Using Advanced Algebra. Doubleday Canada Limited.