Question

Two balls A and B rotate along a circular track. Ball A makes 4 full rotations in 120 seconds. Ball B makes 3 full rotation in 60 seconds. If they start rotating now from the same point, when will they be at the same starting point again?

Answer 1

Find the rate in which both balls make one full rotation around the track.

Ball A:

$120 / 4 = 30$

It takes 30 seconds for Ball A to make a full rotation.

Ball B:

$60 / 3 = 20$

It takes 20 seconds for Ball B to make a full rotation.

Find the least common multiple of 20 and 30 to find the time at which they'll meet.

Multiples of 20: {20,40,60}
Multiples of 30: {30,60}

60 is the least common multiple of both 20 and 30.

The balls will meet again at 60 seconds.