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Bunuel wrote:
Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
A. 8
B. 9
C. 10
D. 11
E. 12
Kudos for a correct solution.
Simply take the LCM of 40 and 45 - you get 360. This is the time they will take to meet for the first time. In this time, Michael would have covered 360/40 = 9 laps.
Answer (B)
The reason for this:
Judging from the question, we know that Michael and Donovan are running in the same direction. When will Michael overtake Donovan? Michael will always be a bit ahead of Donovan and will keep increasing this distance between them till the time he completes one full lap more than Donovan. That is when they will both again be at the starting point together. The time that should have passed at this point should be a multiple of both 40 and 45 so that they are at the starting point. So we find the LCM of 40 and 45 which is 360. In this time, Donovan completes 360/45 = 8 laps and Michael completes 360/40 = 9 laps.
can you please explain to me why it takes Micheal one extra lap (400 meters) to meet Donovan? That is where was the difficulty for me.