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?
Let the first cuckoo came out X times, and the second cuckoo came out Y times. They must cоme out together, so 45x=55у. Х and Y must be equal to the smallest integers. After substitution: Х=11 and Y=9. Inspection: 45*11=55*9=495 minutes. Answer: Both cuckoos came out together after 495 minutes.