Bus A and Bus B leave the bus depot at 6 am. Bus A takes 20 minutes to do its route and bus B takes 35 minutes to complete its route. At what time are they both back at the bus depot together? Give your answer as a 12-hour clock time.

We have been given that Bus A and Bus B leave the bus depot at 6 am. Bus A takes 20 minutes to do its route and bus B takes 35 minutes to complete its route.

We are asked to find the time when the both buses will be back at the bus depot together.

We need to find least common multiple of 20 and 35 to solve our given problem.

Prime factorization of 20: .

Prime factorization of 35:

Least common multiple of 20 and 35 would be .

This means that both buses will be back at the bus depot together after 140 minutes.

Let us convert 140 minutes into hours.

Both buses will be back at the bus depot together after 2 hours  and 20 minutes after 6 am.

Since 2 hours and 20 minutes after 6 am would be 8:20 am, therefore, both buses will be back at the bus depot together at 8:20 am.

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