Bell Ringing Interval
Problem
Six students were given the task of ringing bells at the intervals of 10 seconds, 15 seconds, 30 seconds, 50 seconds, 1 minute and 1.25 minutes, respectively. If they ring bells together at 10 a.m., then how many times will they ring the bell together in the next 3 hours (including the bell rang at 10 a.m.)?
Options:
A) 37 times
B) 31 times
C) 35 times
D) 33 times
Solution
Convert all intervals to seconds: 10, 15, 30, 50, 60, 75.
LCM(10, 15, 30, 50, 60, 75) = 300 seconds = 5 minutes.
In 3 hours = 180 minutes.
Number of times = 180/5 + 1 = 36 + 1 = 37 (including at 10 a.m.).