# Question #de60e

##### 1 Answer

Ken will have run

#### Explanation:

In order for Ken and Hamid to meet again **exactly** on the start line, each must have completed a positive integer ("whole") number of laps, since if they met anywhere else, their current lap would be in progress.

Since time affects both equally, the same amount of time must have passed when they first meet. To find that time, simply take the time in which the **slowest** one (Ken) completes a lap, then see if the other time value divides it perfectly (no remainder, integer quotient). If not, then check the second, third, fourth, etc multiples of Ken's time, and find the first one that is divided by Hamid's time perfectly, or the first (lowest) multiple of

The reason we are doing this, is that if that number is divisible by

Essentially, we are trying to find the least common factor of

Ken will have run