How much time will it take the faster runner to overlap the slower runner?

Question

Brooks and Avery are running laps around the outdoor track, in the same direction. Brooks completes a lap every 78 seconds while Avery needs 91 seconds for every tour of the track. Brooks (the faster runner) has just passed Avery. How much time will it take for Brooks to overtake Avery again?

 

Help would be appreciated!

Answer 1

Note that the two tour times, 78 sec and 91 sec, are in the the proportion of 6:7    [78 = 13 x 6  and 91 = 13 x 7]

 

Brooks, being faster, will complete 7 tours in the same time Avery completes 6 tours.

 

So, both should be shoulder-to-shoulder at 78 x 7 = 546 sec or 91 x 6 = 546 sec