Question

At a bus station, buses begin their routes at 6:00 a.m. The schedule for two of the buses is

based on the time intervals listed below.
Bus A has a long route and leaves the station every 75 minutes.
Bus B has a short route and leaves the station every 15 minutes.
What is the next time Bus A and Bus B will leave the bus station at the same time?
A 7:00 a.m.
B 7:15 a.m.
C 7:30 a.m.
D 8:30 a.m

Answer 1

To find the next time when Bus A and Bus B leave the station at the same time, we need to find the first common multiple of the time intervals of the two buses.

The time intervals for Bus A are 75, 150, 225, 300, and so on.

The time intervals for Bus B are 15, 30, 45, 60, 75, 90, and so on.

The first common multiple of 75 and 15 is 75, so the next time when Bus A and Bus B leave the station at the same time will be 75 minutes after their last common departure time, which was 6:00 a.m.

Therefore, the next time when Bus A and Bus B will leave the bus station at the same time is 7:15 a.m., which is option B.