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?
Answers
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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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.