Question

Bus A and Bus B leave the bus depot at 3 pm.

Bus A takes 25 minutes to complete its route once and bus B takes 30 minutes to complete its route once.
If both buses continue to repeat their route, at what time will they be back at the bus depot together?
Assume the buses have no breaks in between routes.
Give your answer as a 12-hour clock time.

Answer 1

5:30 pm.

Explanation:

First find the LCM (lowest common multiple) of 25 and 30. This is the amount of minutes it will take for the buses to meet again.

25 can be broken up into 5*5

30 can be broken up into 5*6

The most amount of 5s found in a number is two times in 25 and the most amount of 6s found in a number is once in 30, so

25*6=150

150 is the LCM. This means that in 150 minutes, the buses will be back at the bus depot together.

All we have to do now is convert 150 minutes to hours.

One hour is 60 minutes, so 150/60 is 2.5 hours, or 2 hours and 30 minutes.

2 hours and 30 minutes after 3 pm is 5:30 pm.