It takes 36 minutes to manually package 400 candles into boxes for shipment. When an automated packaging system works together with the manual packaging system, 400 candles can be boxed in 9 minutes. How many minutes are required for the automated packaging system working alone to box 400 candles?

12 minutes

Step-by-step explanation:

Candles can be manually packed at the rate of ...

... (400 candles) / (36 minutes) = 11 1/9 candles/minute

The two systems together pack candles at the rate of ...

... (400 candles) / (9 minutes) = 44 4/9 candles/minute

Then the machine's packing rate is the difference between the total and the manual rates:

... machine rate = (44 4/9 candles/minute) - (11 1/9 candles/minute)

... = 33 1/3 candles/minute.

At this rate, the machine working alone can pack 400 candles in ...

... (400 candles) / (33 1/3 candles/minute) = (400 / (100/3)) minutes

... = 400 * 3/100 minutes = 12 minutes