When will beepers beep at the same time

by Moheet
(Hyderabad,Sindh,Pakistan)

Maria has 2 electronic beepers. One beeps after every 5 seconds and the second beeps after every 9 second.

1) At what time both beepers will beep at same same time?

2) How many times will they beep in 1 hour?

3) How many times will they beep at the same time in an hour.


Solution

1)

First beeper beeps every 5 seconds

After 1 minute

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60


Second beeper beeps every 9 seconds

After 1 minute

9, 18, 27, 36, 45, 54, 63,


They will beep at the same time after 45 seconds

To find the next time they will beep, just multiply 45 by 2, 3, 4, 5, and so forth.

For example, the next they will beep at the same time

is 45 × 2 = 90 seconds


2)

How many times will they beep in 1 hour?

First beeper

in 1 minute, the bepper beeps 12 times.

An hour has 60 minutes, so in an hour the beeper will beep 12 × 60 times or 720 times


Second beeper


in 54 seconds, the bepper beeps 6 times.

in 9 seconds, the beeper beeps 1 time (Divide 54 and 6 by 6)

in 1 second, the beeper beeps 1/9 time


An hour has 60 minutes or 3600 seconds

If 1 second is 1/9

3600 seconds is 3600 × 1/9 = 3600 / 9 = 400


The second beeper will beep 400 times


3)

The pattern below shows the times they will beep at the same time for 1 hour or 3600 second. There are 80 such numbers.

45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990, 1035, 1080, 1125, 1170, 1215, 1260, 1305, 1350, 1395, 1440, 1485, 1530, 1575, 1620, 1665, 1710, 1755, 1800, 1845, 1890, 1935, 1980, 2025, 2070, 2115, 2160, 2205, 2250, 2295, 2340, 2385, 2430, 2475, 2520, 2565, 2610, 2655, 2700, 2745, 2790, 2835, 2880, 2925, 2970, 3015, 3060, 3105, 3150, 3195, 3240, 3285, 3330, 3375, 3420, 3465, 3510, 3555, 3600.


You can find the answer quicker by doing 45 × ? = 3600

Just divide 3600 by 45 to get 80.

They will beep at the same time 80 times in that hour.