Final answer:
The signals A, B, and C will beep at the same time 12 times in one hour.
Step-by-step explanation:
To find out how many times the three signals (A, B, and C) will beep at the same time in one hour, we need to determine the least common multiple (LCM) of their beep intervals.
The LCM of 25, 30, and 100 seconds can be calculated by finding the prime factorization of each number. The prime factorization of 25 is 5^2, of 30 is 2 * 3 * 5, and of 100 is 2^2 * 5^2.
Now, we take the highest powers of each prime factor: 2^2, 3, and 5^2. Multiplying these, we get 2^2 * 3 * 5^2 = 4 * 3 * 25 = 300.
So, the LCM of the three signals' beep intervals is 300 seconds.
To find how many times they beep in one hour (3600 seconds), we divide 3600 by the LCM: 3600 / 300 = 12.
Therefore, the signals A, B, and C will beep at the same time 12 times in one hour.
Your question is incomplete, most probably the complete question is:
Signal A beeps every 25 seconds Signal B beeps every 30 seconds. Signal C beeps every 100 seconds. The three signals start beeping at the same time. How many times in one hour will the three signals beep at the same time?