One alarm beeps 4 seconds after it is activated and at the end of every 6 seconds after that. Another alarm beeps 29 seconds after it is activated and at the end of every 30 seconds after that. The 2 alarms are activated at the same time and are left on for \(t\) minutes, where t is a whole number. What is the total number of times the 2 alarms beep in those \(t\) minutes?

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The first alarm will beep at the end of:

$$ 4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70... $$

Note that the sequence has 10 terms in the first minute (4-58s), and then repeats (64-118).

The second alarm will beep at the end of:

$$ 29, 59, 89, 119.. $$

Note that every minute, 2 beeps occur.

Therefore, \(10+2=12\) beeps will occur every minute.