Question

Bus A and Bus B leave the bus depot at 7 am.
Bus A takes 25 minutes to complete its route once and bus B takes 40 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.
am

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Bus A and Bus B leave the bus depot together at 7 am.

The time taken by both the buses to come back at the bus depot together will be equal to the LCM (largest common multiple) of the time taken by Bus A and Bus B.

The prime factorization of 25 and 40 are

\begin{gathered}25=5\times5,\\\\40=2\times2\times2\times5.\end{gathered}25=5×5,40=2×2×2×5.

So,

LCM(25,40)=2\times2\times2\times5\times5=200.LCM(25,40)=2×2×2×5×5=200.

200 minutes = 3 hours 20 minutes.

Therefore, the buses will come back at the bus depot at

7~\textup{AM}+3~\textup{hours }20~\textup{minutes}=10:20~\textup{AM}.7 AM+3 hours 20 minutes=10:20 AM.

Thus, bus A and bus B both come back at 10:20 AM.