Question

One timer is set to ring every 48 seconds. Another timer is set to ring every 2 minutes 15 seconds. They rang together at 7 p.m. When is the next time that the timers will ring together? Include your reasoning and calculations to justify your answer

Answer 1

Answer:

8:16 p.m.

Step-by-step explanation:

You have to find LCM(a,b), where a=48 seconds and b=95 seconds (2 minutes 15 seconds).

1.

$48=2\cdot 24=2\cdot 2\cdot 12=2\cdot 2\cdot 2\cdot 6=2\cdot 2\cdot 2\cdot 2\cdot 3=2^4\cdot 3.$

2.

$95=5\cdot 19.$

3.

$LCM(48,95)=2^4\cdot 3\cdot 5\cdot 19=4560\text{ seconds }=76\text{ minutes }=1\text{ hour }16 \text{ minutes. }$

If they rang together at 7 p.m, then the next time that the timers will ring together will be after 1 hour 16 minutes that is 8:16 p.m.