A grandfather clock chimes 4 times when it is fifteen minutes after the hour,8 Times On the half hour,and on the hour it chimes 16 plus it chimes the number of times equal to the hour.in one year how many chimes are struck by the grandfather clock?

Question

A grandfather clock chimes 4 times when it is fifteen minutes after the hour,8 Times On the half hour,and on the hour it chimes 16 plus it chimes the number of times equal to the hour.in one year how many chimes are struck by the grandfather clock?

Answer 1

Does it chime on the 3/4 hour?

Answer 2

24h/day * 365days/yr. * 60min/h = 525,600 min/yr.

( 525,600/15) *4 = The number of chimes/yr.

(45/15) * 4 = The number of chimes in 3/4 hour(45min).

Answer 3

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Answer 4

To find the total number of chimes struck by the grandfather clock in one year, we need to calculate the chimes for each hour, plus the chimes for each 15-minute interval.

Let's break it down step by step:

1. Chimes on the hour: The grandfather clock chimes 16 times on the hour.
For each hour of the day (24 hours), it chimes 16 times, so we have 24 * 16 = 384 chimes for the hour chimes.

2. Chimes on the half-hour: The grandfather clock chimes 8 times on the half-hour.
For each hour of the day (24 hours), it chimes 8 times on the half-hour, so we have 24 * 8 = 192 chimes for the half-hour chimes.

3. Chimes on the 15-minute intervals: The grandfather clock chimes 4 times when it is 15 minutes past the hour.
For each hour of the day (24 hours), there are 3 intervals (45 minutes, 30 minutes, and 15 minutes past the hour) where it chimes 4 times.
So, we have 24 * 3 * 4 = 288 chimes for the 15-minute interval chimes.

4. Chimes for the number of times equal to the hour: The grandfather clock chimes the number of times equal to the current hour.
This means that for each hour (24 hours), it chimes the number of times equal to the hour. So, we have 24 + 23 + 22 + ... + 1 chimes.
To find the sum of the numbers from 1 to 24, we can use the formula: sum = (n / 2) * (first number + last number) = (24 / 2) * (1 + 24) = 12 * 25 = 300 chimes.

To calculate the total number of chimes, we sum up all the chimes from the above steps:
384 + 192 + 288 + 300 = 1164 chimes in one day.

Since we want to calculate for a whole year, we multiply the daily chimes by the number of days in a year, which is 365:
1164 * 365 = 425,460 chimes in one year.

Therefore, the grandfather clock strikes 425,460 times in one year.