Question

Bus A and Bus B leave the bus depot at 9 am. Bus A takes 30 minutes to do its route and bus B takes 40 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

Final Answer:

The time at which both the buses A and B are back at the bus depot together, after leaving the bus depot at 9 am and Bus A takes 30 minutes to do its route while bus B takes 40 minutes to complete its route, is at every two hours, that is, 11 am, 1 pm, 3pm, 5pm, 7pm, 9pm, 11pm and so on till the depot closes the bus journeys.

Given:

Bus A and Bus B leave the bus depot at 9 am. Bus A takes 30 minutes to do its route and bus B takes 40 minutes to complete its route. Give your answer as a 12-hour clock time.

To Find:

The time at which both the buses A and B are back at the bus depot together.

Explanation:

The Least Common Multiple (LCM) of any count of numbers indicates the lowest value of multiple that is divided by all the numbers considered.

It is very useful to find the solution to the problems as given here.

The relation between hour and minute is that sixty minutes make one hour.

Step 1 of 3

Since, both the buses A and B leave the bus depot at 9 am, it is evident that the time at which both the buses A and B are back at the bus depot together is the LCM of the time taken by the buses A and B individually to complete the route and back at the same depot.

Step 2 of 3

As Bus A takes 30 minutes while bus B takes 40 minutes to complete the route starting from and coming back at the same depot, the LCM of 30 minutes and 40 minutes is calculated as follows.

$30=2 \times 3 \times 5\\40=2 \times2 \times 2 \times 5\\LCM\; of\; 30,\;40\;=2\times2\times2\times3\times5=120$

Step 3 of 3

As the LCM of 30 minutes and 40 minutes is 120 minutes or 2hours, the time at which both the buses A and B are back at the bus depot together, after leaving the bus depot at 9 am happens at every two hours, that is, 11 am, 1 pm, 3pm, 5pm, 7pm, 9pm, 11pm and so on till the depot closes the bus journeys.

Therefore, the time at which both the buses A and B are back at the bus depot together, after leaving the bus depot at 9 am , where Bus A takes 30 minutes and bus B takes 40 minutes to complete the routes, is at every two hours, that is, 11 am, 1 pm, 3pm, 5pm, 7pm, 9pm, 11pm and so on till the depot closes the bus journeys.

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