Question

Starting at 6am a bus makes a stop on 1st ave every 8 mins another bus that also starts at 6am makes a stop on 1st ave every 12 mins how many times in a hour will the two buses make a stop at the same time at what time will the two buses make a stop at the same

Answer 1

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Answer:

2.5 times per hour, on average

{0:00, 0:24, 0:48, 1:12, 1:36} then repeating at 2:00

Explanation:

The least common multiple of the intervals is ...

LCM(8, 12) = 8·12/GCD(8, 12) = 8·12/4 = 24

The two buses will stop at the same time every 24 minutes. That is 60/24 = 2.5 times per hour.

Starting with the 6:00 am stop, the next joint stop is at 6:24, then 6:48. In the next hour, the stops are at 7:12 and 7:36. This sequence of times repeats, starting at 8:00 am. That is, the cycle repeats every 2 hours.