A factory whistle blows every 30 minutes. The clock tower chimes every 15 minutes. If they both sounded at 1:00 p.m., at what time will you hear them both at the same time again?
1:30
1:45 because 30 plus 15 equals 45
To determine when you will hear both the factory whistle and the clock tower chime at the same time again, we need to find the least common multiple (LCM) of the two time intervals.
The factory whistle blows every 30 minutes and the clock tower chimes every 15 minutes.
To find the LCM, we can list out the multiples of each time interval until we find a common multiple:
Multiples of 30 minutes: 30, 60, 90, 120, 150, 180, ...
Multiples of 15 minutes: 15, 30, 45, 60, 75, 90, 105, 120, ...
From the lists above, we can see that the first common multiple is 60 minutes, as both 60 minutes and 30 minutes are on the first list, and both 60 minutes and 15 minutes are on the second list.
Therefore, the factory whistle and the clock tower will sound at the same time again after 60 minutes, or 1 hour, from the initial 1:00 p.m. This means you will hear them both at the same time again at 2:00 p.m.