# Math Help - Two Cuckoo Clocks

1. ## Two Cuckoo Clocks

I have a maths problem and wanted to know if there was an easier way or a formula to work it out, rather than go through each time which is taking ages.

Problem - "Two cuckoo clocks were brought to the Tick Tock Clock Shop for repairs. Both clocks always told the correct time. However, one cuckoo came out every 45 minutes and the other came out every 55 minutes. One day, both cuckoos came out at 12.00 noon. When was the next time both cuckoos came out together."

If someone knows a way of working it out, that would be great. Thanks.

2. List the times of both clocks until they match

$C_{45}: 12,12:45,1:30,2:15,\dots$

$C_{55}: 12, 12:55,1:50,2:45,\dots$

3. Originally Posted by stormtigershark
I have a maths problem and wanted to know if there was an easier way or a formula to work it out, rather than go through each time which is taking ages.

Problem - "Two cuckoo clocks were brought to the Tick Tock Clock Shop for repairs. Both clocks always told the correct time. However, one cuckoo came out every 45 minutes and the other came out every 55 minutes. One day, both cuckoos came out at 12.00 noon. When was the next time both cuckoos came out together."

If someone knows a way of working it out, that would be great. Thanks.
Take LCM(45,55) = 495.

Then see that 495 = 8*60 + 15, meaning 8 hrs 15 minutes.

So, that makes 8:15 PM.

4. Originally Posted by pickslides
List the times of both clocks until they match

$C_{45}: 12,12:45,1:30,2:15,\dots$

$C_{55}: 12, 12:55,1:50,2:45,\dots$

Thanks, but that's what I was originally doing. I wanted to know if there was a quicker way or a formula for this type of question.

5. Originally Posted by undefined
Take LCM(45,55) = 495.

Then see that 495 = 8*60 + 15, meaning 8 hrs 15 minutes.

So, that makes 8:15 PM.

Thanks for the formula.

6. Originally Posted by stormtigershark
"Two cuckoo clocks were brought to the Tick Tock Clock Shop for repairs.
Ad for Tick Tock Clock Shop: "If your clock don't tick, tock to us !"

7. Originally Posted by stormtigershark
Thanks for the formula.
Its not a formula, merely another method