Question

Bus A and Bus B leave the bus depot at 7 am.
Bus A takes 25 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?

Answer 1

$\fontsize{18}{10}{\textup{\textbf{Bus A and bus B both come back at 10:20 AM.}}}$

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

$25=5\times5,\\\\40=2\times2\times2\times5.$

So,

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

200 minutes = 3 hours 20 minutes.

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

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

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

Answer 2

Given : 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.

To find : at what time will they be back at the bus depot together?

Solution:

Bus A takes 25 minutes to complete its route once

Bus B takes 40 minutes to complete its route

To find time when they will be back at the bus depot together we need to find LCM of 25 & 40 Minutes

25 = 5 * 5

40 = 2 * 2 * 2 * 5

LCM = 2 * 2 * 2 * 5 * 5

= 200

After 200 minutes  Buses will be back at the bus depot together

200 minutes = 3 hr 20 Minutes

7 : AM  +  3 hr 20 Minutes

= 10 : 20 AM

At 10 : 20 AM Buses be back at the bus depot together

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