In a school, one bell rings after every 30 minutes while the other rings after every 35 minutes. If the two bell rang together at 8:15 a. m., at what. Time did they ring together next?
oops. R_scott was right. I guess I better clean my glasses.
LCM(35,90) = 630
so what is 630 minutes after 8:15 ?
7 * 30 = 6 * 35 = 210
210 minutes after 8:15 a.m.
To find out when the two bells will ring together again, we need to determine the least common multiple (LCM) of the intervals between each bell ring.
In this case, the intervals between the bell rings are 30 minutes and 35 minutes.
To find the LCM, we can follow these steps:
Step 1: Find the multiples of each interval until we find a common multiple.
- Multiples of 30 minutes: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300...
- Multiples of 35 minutes: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350...
Step 2: Identify the first common multiple from the lists above.
The first common multiple of 30 and 35 is 210 minutes.
Step 3: Convert the common multiple to hours and minutes.
Since there are 60 minutes in an hour:
210 minutes = 3 hours + 30 minutes.
Step 4: Add the time from the initial bell ring.
If the bells rang together at 8:15 a.m., we add 3 hours and 30 minutes to this time:
8:15 a.m. + 3 hours + 30 minutes = 11:45 a.m.
Therefore, the bells will ring together next at 11:45 a.m.