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

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?

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Nevaeh 3 weeks 2021-10-05T05:24:40+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-05T05:26:29+00:00

    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

    Learn More:

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    0
    2021-10-05T05:26:33+00:00

    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.

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