bus a stops every 12 minutes and bus b stops every 9 minutes on the same circuit.they stop at the same bus 9:15.when is the next time this happens?

What is the least common multiple of 12 and 9?

No.

Multiples of 9:
9, 18, 27, 36, 45, 54, etc.

Multiples of 12?

12,24......

Keep going until you find the common multiple.

36?

Yes. The next time they're together at that stop will be 36 minutes later.

To find out when the next time the buses stop at the same time, we need to determine the least common multiple (LCM) of the two intervals.

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, ...

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ...

From the list, we can see that the least common multiple of 12 and 9 is 36. This means that Bus A and Bus B will meet at the same bus stop every 36 minutes.

Since they both stop at 9:15, we need to calculate how many minutes have passed since then until the next occurrence of 36 minutes. We can subtract 15 from 36, which gives us 21 minutes.

Therefore, the next time both Bus A and Bus B stop at the same time will be 21 minutes past 9:15.

To calculate the exact time, we add 21 minutes to 9:15.

9:15 + 0:21 = 9:36

So, the next time both buses A and B will stop at the same time will be at 9:36.