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  3. In a factory, machine A operates on a cycle of 20 hours of work followed by 4 ho

In a factory, machine A operates on a cycle of 20 hours of work followed by 4 ho

游客2025-02-24  44
问题 In a factory, machine A operates on a cycle of 20 hours of work followed by 4 hours of rest, and machine B operates on a cycle of 40 hours of work followed by 8 hours of rest. Last week, the two machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. On which days during that time period was there a time when both machines were at rest?
Indicate all such days.
A Monday
B Tuesday
C Wednesday
D Thursday
E Friday
F Saturday
选项
答案 C，E
解析 Both machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. Note that 1 day has 24 hours and 2 days have 48 hours.
Machine A operates on a cycle of 20 hours of work followed by 4 hours of rest, so it was at rest from 8 o’clock in the morning until 12 noon every day from Tuesday to Saturday.
Machine B operates on a cycle of 40 hours of work followed by 8 hours of rest, so it was at rest from 4 o’clock in the morning until 12 noon on Wednesday and Friday.
Thus both machines were at rest from 8 o’clock in the morning until 12 noon on Wednesday and Friday. The correct answer consists of Choices C and E.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 7: Find a Pattern
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