Question

Maria has two electronic beepers, beeping every 4 and 9 seconds respectively. How many times during the next hour will both beepers beep simultaneously?

a) 5
b) 6
c) 7
d) 8

Answer 1

To find the number of times both beepers will beep simultaneously in the next hour, we need to find the least common multiple of their beep intervals, which is 36 seconds. Then, divide the total number of seconds in an hour by the LCM to find the number of times the beepers will beep together, which is 100.

Step-by-step explanation:

To find how many times the two beepers will beep simultaneously, we need to find the least common multiple (LCM) of their beep intervals. The LCM of 4 and 9 is 36, which means that both beepers will beep together every 36 seconds.

Next, we need to find how many times the beepers will beep in one hour. There are 60 minutes in one hour, and 60 seconds in one minute, so there are 60 * 60 = 3600 seconds in one hour.

To find the number of times the beepers will beep in one hour, we divide 3600 by 36, which gives us 100. Therefore, the beepers will beep simultaneously 100 times in the next hour.