Question

Bus A and Bus B leave the bus depot at 5 pm. Bus A takes 30 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.

Answer 1

8:30 pm

Explanation:

step 1

Decompose the numbers in prime factors

`30=(2)(3)(5)\\35=(5)(7)`

step 2

Find the LCM

The LCM of 30 min and 35 minutes will be given as

`LCM=(2)(3)(5)(7)=210\ min`

step 3

Adds 210 minutes to the starting time

First, converting 210 minutes to hours

Remember that

`1\ h=60\ min`

will need dividing 210 by 60

`210/60=3.5\ h`

therefore

5:00 pm+3.5 h=8:30 pm