Two bus services A&B arrive at the station. service A arrives every 15 minutes, service B arrives every 20 minutes. The first bus arrives at 8 o'clock. When will both buses arrive at the station again?
Two bus services A&B arrive at the station. service A arrives every 15 minutes, service B arrives every 20 minutes. The first bus arrives at 8 o'clock. When will both buses arrive at the station again?
i do not know how to do this its kind f hard I need some help figuring this out
9:oo or 69 minutes
What is the least common multiple of 15 and 20?
To find when both buses will arrive at the station again, we need to find the least common multiple (LCM) of their arrival times.
First, let's list the arrival times for each bus:
Bus service A: 8:00, 8:15, 8:30, 8:45, 9:00, 9:15, ...
Bus service B: 8:00, 8:20, 8:40, 9:00, 9:20, 9:40, ...
From observing the two lists, we can see that the first time both buses arrive at the same time is 9:00. However, to be sure, we can calculate the LCM of 15 and 20.
To find the LCM, we can use the prime factorization method:
15 = 3 x 5
20 = 2 x 2 x 5
Now, take the highest power of each prime factor that appears in either factorization:
2 x 2 x 3 x 5 = 60
Therefore, the LCM of 15 and 20 is 60 minutes. This means that both buses will arrive at the station again in 60 minutes.
Adding 60 minutes to the first arrival time of service A at 8:00, we get 9:00. So both buses will arrive at the station again at 9 o'clock.