A bell rings every 20 seconds. A second bell rings every 25 seconds. A third bell rings every 30 seconds. They all ring together at 8 p.m. how long will it be before all three bells ring together again?
To find the time it takes for all three bells to ring together again, we need to find the least common multiple (LCM) of their ringing times.
The LCM of 20, 25, and 30 is 300.
Therefore, all three bells will ring together again after 300 seconds.
Since there are 60 seconds in a minute, 300 seconds is equal to 300/60 = 5 minutes.
Therefore, all three bells will ring together again after 5 minutes.
To find out how long it will be before all three bells ring together again, we need to find the LCM (Least Common Multiple) of the three given time intervals: 20 seconds, 25 seconds, and 30 seconds.
To find the LCM of these numbers, we can start by listing their multiples and look for the first common multiple.
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, ...
Multiples of 25: 25, 50, 75, 100, 125, 150, ...
Multiples of 30: 30, 60, 90, 120, 150, ...
The first common multiple is 100 seconds, so it will take 100 seconds for all three bells to ring together again.
However, we need to convert this answer to a time format. Since each bell starts ringing at 8 p.m., we need to add the time it takes for 100 seconds to pass from 8 p.m.
100 seconds is equal to 1 minute and 40 seconds, so all three bells will ring together again 1 minute and 40 seconds after 8 p.m.