QQuestionMathematics
QuestionMathematics
Using a 5 -minute and an 8 -minute hourglass timer, how can you measure 1 minute? Explain your method.
A. Start both hourglasses at the same time. When the 5 -minute hourglass runs out, turn it over. When the 8 -minute hourglass runs out, flip it. When the 5 -minute hourglass runs out again, 1 minute has passed.
B. Start both hourglasses at the same time. When the 8 -minute hourglass runs out, turn it over. When the 5 -minute hourglass runs out, 1 minute has passed.
C. Start both hourglasses at the same time. When the 8 -minute hourglass runs out, 1 minute has passed.
D. Start both hourglasses at the same time. When the 5 -minute hourglass runs out, 1 minute has passed.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the Problem
We need to use a 5 -minute and an 8 -minute hourglass to measure exactly 1 minute. This requires careful timing and flipping of the hourglasses.
Step 3:: Analyze the Possible Solutions
Let's examine each option carefully: Option A: - Start both hourglasses simultaneously - When 5 -minute hourglass runs out, turn it over - When 8 -minute hourglass runs out, flip it - When 5 -minute hourglass runs out again, 1 minute has passed
Step 4:: Verify Option A
Let's track the timing: - At 0 minutes: Both hourglasses start - At 5 minutes: 5 -minute hourglass runs out - At 8 minutes: 8 -minute hourglass runs out - At 10 minutes: 5 -minute hourglass runs out again
Step 5:: Calculate the Time Difference
10 - 8 = 2 \text{ minutes}
This means Option A does NOT measure exactly 1 minute.
Step 6:: Examine Other Options
- Option B: Incorrect method - Option C: Incorrect method - Option D: Incorrect method
Step 7:: Correct Solution
The correct method is Option B: - Start both hourglasses simultaneously - When the 8 -minute hourglass runs out, turn it over - When the 5 -minute hourglass runs out, exactly 1 minute has passed Verification: - At 0 minutes: Both hourglasses start - At 5 minutes: 5 -minute hourglass runs out - At 8 minutes: 8 -minute hourglass runs out - At this point, exactly 1 minute has elapsed since the 5 -minute hourglass ran out
Final Answer
Option B is the correct method to measure 1 minute using a 5 -minute and an 8 -minute hourglass.
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