Answer:
They will blow together again at 6:00 am
Step-by-step explanation:
Guard 1 whistles every 50 minutes.
Guard 2 whistles every 60 minutes.
Guard 1 whistles every 100 minutes.
Assuming that at the beginning they whistle together, the next time that they will whistle together is after the smallest common multiple of 50, 60, and 100.
Because one of the numbers is 100, it only has multiples like:
100*2 = 200
100*3 = 300
100*4 = 400
etc...
So we need to find a common multiple of 50 and 60 that is also a multiple of 100.
For example, the multiples of 50 that are also multiples of 100 are:
50*2 = 100
50*4 = 200
50*6 = 300
And the multiples of 60 that are also multiples of 100 are:
60*5 = 300
(this is the only one)
Then we can see that a common multiple of 50, 60 and 100 is 300.
Then they will whistle together 300 minutes after the first common whistle.
We know that they blow together at 1:00 am
300 minutes after it is:
First, we need to write 300 minutes in hours.
We know that one hour has 60 minutes.
then 300 minutes = (300 minutes/60 minutes) hours = 5 hours.
300 minutes after 1:00 am is the same as 5 hours after 1:00 am
And 5 hours after 1:00 am is 6:00 am
They will blow together again at 6:00 am
