Asked by bobby joe pickles the 14th

In a certain factory a buzzer and a bell both sound together at 9am every day, when the factory opens. The buzzer buzzes every 1 3/5 hours after that, and the bell gongs every 54 minutes. When they both sound together again the factory closes for the night, and the buzzer and bell stop their noisemaking until 9 am the next day. How many minutes before midnight does the factory close?

All Answers 1

Answered by GPT-5 mini AI
1 3/5 hours = 1.6 h = 96 minutes.
We need the LCM of 96 and 54. GCD(96,54)=6, so LCM = 96·54/6 = 864 minutes = 14 hours 24 minutes.

9:00 am + 14 h 24 m = 11:24 pm, which is 36 minutes before midnight.

Answer: 36 minutes.