Bus A leaves interchange 6 minutes, Bus B leaves 12 minutes later, Bus C leaves 18 minutes later. If all buses leave at 6 am when will all 3 buses leave at the same time again. Kindly show workings and explantion to problem. Thank you
express 5 minutes 15 seconds in seconds
To find the time at which all three buses will leave at the same time again, we need to find the least common multiple (LCM) of the time intervals between each bus.
Let's calculate the time intervals:
Interval between Bus A and Bus B = Time when Bus B leaves - Time when Bus A leaves
Interval between Bus B and Bus C = Time when Bus C leaves - Time when Bus B leaves
Given:
Bus A leaves 6 minutes past 6 am
Bus B leaves 12 minutes after Bus A = 6 + 12 = 18 minutes past 6 am
Bus C leaves 18 minutes after Bus B = 18 + 18 = 36 minutes past 6 am
Now, let's calculate the time intervals:
Interval between Bus A and Bus B = 18 minutes - 6 minutes = 12 minutes
Interval between Bus B and Bus C = 36 minutes - 18 minutes = 18 minutes
To find the LCM of these time intervals (12 and 18 minutes), we can list out the multiples of both numbers:
Multiples of 12: 12, 24, 36, 48, 60, ...
Multiples of 18: 18, 36, 54, 72, 90, ...
The LCM is the smallest number that is a multiple of both numbers. In this case, it is 36 minutes.
So, all three buses will leave at the same time again after 36 minutes past 6 am.
Explanation:
The LCM is used to find the smallest common multiple of two or more numbers. In this problem, we need to find the time at which all three buses leave at the same time again. To do this, we calculate the time intervals between each bus. Then, we find the LCM of these time intervals. The LCM represents the smallest time interval in which all three buses will align their departure times.