buses to the stadium leave central station every 10 minutes buses to the zoo leave central station every 16 minutes both buses leave central station at 4 p.m. find the next time both buses will leave central station at the same time.
buses to stadium leave :10 20 30 40 50 60 70 80 90 ....
buses to zoo leave 16 32 48 64 80 96 ....
ahhh, looks like we need the lowest common multiple.
5:20 pm minutes after 4:00 pm
To find the next time both buses will leave Central Station at the same time, we need to determine the least common multiple (LCM) of the intervals between their departures.
The intervals between the departures of the stadium bus is 10 minutes, and the intervals between the departures of the zoo bus is 16 minutes.
To find the LCM of 10 and 16, we can list the multiples of the larger number until we find a multiple that is also divisible by the smaller number.
Multiples of 16: 16, 32, 48, 64, 80, 96, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
From the list, we can see that 80 is divisible by both 10 and 16.
Therefore, the next time both buses will leave Central Station at the same time is 80 minutes (or 1 hour and 20 minutes) after their current departure time of 4 p.m.
So, the next time both buses will leave Central Station at the same time is 5:20 p.m.
To find the next time both buses will leave the central station at the same time, we need to determine the time interval at which their departure times coincide.
The time interval at which the buses' departure times coincide is known as the least common multiple (LCM) of their departure intervals. In this case, the departure intervals are 10 minutes for the stadium and 16 minutes for the zoo.
To find the LCM of two numbers, you can use various methods. One common approach is to list the multiples of each number until you find a common multiple. Let's use this method:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, ...
From the lists above, we can see that the first common multiple is 80. Therefore, the buses will leave the central station at the same time after 80 minutes.
Since both buses left at 4 p.m., we need to determine the time when 80 minutes have elapsed. Adding 80 minutes to 4 p.m.:
4 p.m. + 80 minutes = 5:20 p.m.
Therefore, the next time both buses will leave the central station at the same time is 5:20 p.m.