It takes Megan 7 minutes to run a mile, and it takes Mike 8 minutes. If Megan and Mike both begin running at exactly 8:00 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
Choices:
A) 8:28 am
B) 8:35 am
C) 8:42 am
D) 8:49 am
E) 8:56 am
Since Megan will run s miles after s × 7 minutes and Mike will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 7 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 7 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 7 and 8 is 56, so in the context of the question, this would be 56 minutes. Therefore, the first time they will finish running a mile at the same time is 8:00 + 56 minutes, or 8:56 a.m. The answer is (8:56 am).
<result>E</result>
It takes Megan 7 minutes to run a mile, and it takes Mike 8 minutes. If Megan and Mike both begin running at exactly 8:00 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?