It takes Jake 15 minutes to do one oil change, and it takes Bob 10 minutes. If Jake and Bob both begin doing oil changes at exactly 10:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously? Choose the correct choice.
A) 10:00 a.m. B) 10:15 a.m. C) 10:30 a.m. D) 10:45 a.m. E) 11:00 a.m.
Since Jake will finish s oil changes after s × 15 minutes and Bob will finish c oil changes after c × 10 minutes, they both will finish doing an oil change at the same time when s × 15 = c × 10. 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 15 and 10. The question asks for the first time they will finish a car simultaneously, so you must find the least common multiple. The least common multiple of 15 and 10 is 30, so in the context of the question, this would be 30 minutes. Therefore, the first time they will finish changing the oil of a car at the same time is 10:00 + 30 minutes, or 10:30 a.m. The answer is (10:30 a.m.).
<result>C</result>
It takes Jake 15 minutes to do one oil change, and it takes Bob 10 minutes. If Jake and Bob both begin doing oil changes at exactly 10:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?