Question :
(3.) A bus service centre has 2 feed services that start together at 8 a.m. Bus A leaves at,in 15 minutes interval, while bus B leaves at 20 minutes interval. On a particular day, howmany times do both services leave together from 8 a.m. to 11 a.m.?
LCM(15,20) = 60
So, they leave together once an hour.
Now finish it off.
Ans
To find out how many times both bus services leave together from 8 a.m. to 11 a.m., we need to determine the number of times their departure times coincide.
We can solve this problem by finding the least common multiple (LCM) of the two intervals, which will give us the pattern of when both buses leave together.
First, let's find the LCM of 15 and 20. We can do this by listing the multiples of each number until we find a common multiple:
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300
Based on the above lists, we can see that 60 is the least common multiple of 15 and 20 because it's the smallest number that appears in both lists.
Since the LCM of 15 and 20 is 60, both bus services will leave together every 60 minutes. Therefore, we need to determine how many times 60 minutes (1 hour) fits within the 3-hour period from 8 a.m. to 11 a.m.
Dividing the 3-hour period (180 minutes) by the interval of 60 minutes, we get:
180 minutes / 60 minutes = 3
So, both bus services will leave together 3 times from 8 a.m. to 11 a.m.