It takes Beth 9 minutes to do one oil change, and it takes Logan 12 minutes. At 4:56 pm, they both finish an oil change simultaneously. If Beth and Logan both began doing oil changes at exactly the same time and worked without pausing, when did they both start doing oil changes?  Pick one:
A) 4:11 pm
B) 4:20 pm
C) 4:29 pm
D) 4:38 pm
E) 4:47 pm
Since Beth finishes s oil changes after s × 9 minutes and Logan finishes c oil changes after c × 12 minutes, they both finished doing an oil change at the same time when s × 9 = c × 12. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 9 and 12. The question asks for the first time they began a car simultaneously, so you must find the least common multiple and subtract. The least common multiple of 9 and 12 is 36, so in the context of the question, this would be 36 minutes. Therefore, they began changing the oil of a car at the same time at 4:56 - 36 minutes, or 4:20 p.m. The answer is (4:20 pm).
<result>B</result>
It takes Beth 9 minutes to do one oil change, and it takes Logan 12 minutes. At 4:56 pm, they both finish an oil change simultaneously. If Beth and Logan both began doing oil changes at exactly the same time and worked without pausing, when did they both start doing oil changes?