James has two malfunctioning robots. One of theme beeps every 4 seconds; the other beeps every 9 seconds. If they are turned on at exactly the same time, how many times during the next hour will both robots beep at the same time?
The first one beeps when multiples of 4 seconds have passed, when these
numbers of seconds have passed:
4,8,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,...
The second one beeps when multiples of 9 seconds have passed, when these
numbers of seconds have passed:
9,18,27,36,45,54,63,72,81...
They will beep together when the numbers of seconds have passed which
are common multiples of both 4 and 9. which are the multiples of their
LCM, which is 36.
Now we need to find how many multiples of 36 seconds there are in
an hour.
An hour is 60 minutes long and each minute is 60 seconds long, so
1 hour is 3600 seconds long. We divide 3600 by 36 and get 100.
So they will beep together 100 times in the next hour.
Edwin
