Question

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?

Answer 1

12 minutes

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