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Difficulty: MediumTime Measurements and Calculations

A specialized water purification system takes 33 hours and 2020 minutes to process one complete cycle. If an engineering detachment runs the system continuously for exactly 2.52.5 days, how many complete cycles will the system finish?

Answer: 18 cycles

Answer

18
The correct answer is found by establishing a common unit of time (minutes) for both the total duration and the cycle length. First, converting the 2.52.5 days of total operation into hours gives 6060 hours, which equals 36003600 minutes. Next, converting the 33 hour and 2020 minute cycle duration into minutes yields 200200 minutes. Finally, dividing the total available time (36003600 minutes) by the cycle time (200200 minutes) results in exactly 1818 complete cycles.

Step-by-Step Solution

1
Convert the total continuous running time from days to hours.
2.5×24=602.5 \times 24 = 60 hours
To establish a smaller standard unit of time to match the cycle duration.
2
Convert the total operating hours into minutes.
60×60=360060 \times 60 = 3600 minutes
Minutes will serve as the common baseline unit for the calculation.
3
Convert the required time for a single cycle into minutes.
3×60=1803 \times 60 = 180 minutes; 180+20=200180 + 20 = 200 minutes
To express the cycle duration in the exact same unit as the total running time.
4
Calculate the total number of completed cycles by dividing the total minutes by the cycle minutes.
3600÷200=183600 \div 200 = 18 cycles
This division determines how many 200200-minute intervals fit within the 36003600-minute window.

Key Concept

Multi-step time unit conversions and calculating work rate.
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Topics

Time Measurements and Calculations

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