A clock chimes every hour. The clock chimes at 1 o'clock, twice at 2 o'clock, and so on.
A. How many times will the clock chime from 1 p.m. through midnight? in exactly one 24-hour period.
B. Another clock also chimes once on every half hour. How does this affect the sequence and the total number of chimes per day?
Answers
other clock struck once in every half hour. There are 24 half hours in a day. therefore the total chimes is 90 times
Answer:
(1) 156
(2) 312
Given:
A clock chimes every hour. The clock chimes at 1 o'clock, twice at 2 o'clock, and so on.
To find:
A. How many times will the clock chime from 1 p.m. through midnight? in exactly one 24-hour period.
B. Another clock also chimes once on every half hour. How does this affect the sequence and the total number of chimes per day?
Solution:
(1)
The clock has 12 hours, therefore, there will be two rounds of clock per day.
When it is written in an arithmetic series:
1,2,3,4,....,12
We know that the sum of an arithmetic series with first term a and common difference d is
Sn = n/2 [2a+(n−1)d]
Now to find the sum of series, substitute n=12,a=1 and d=2−1=1 in Sn = n/2 [2a+(n−1)d] as follows:
S 12=
12/2 [(2×1)+(12−1)1]=6[2+(11×1)]=6(2+11)=6×13=78
Therefore, it will strike 78 times in 12 hours.
Now to find the number of times it will strike in full day that is in 24 hours is 2×78=156.
Hence, the clock strikes 156 times in a day.
(2)
For the clock which chimes once on every half hour = 156 × 2 = 312 times a day.
Conclusion:
For the clock which chimes once on every hour has 156 chimes .
For the clock which chimes once on every half hour has total of 312 chimes in a day .
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