Right angle between 4:30 and 5:00 (repaired): At what time between 4:30 and 5:00 will the hands of a clock be at a right angle?
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A50 minutes past 4
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B42 minutes past 4
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C54 6/11 minutes past 4
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D46 minutes past 4
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ENone of these
Answer
Correct Answer: 54 6/11 minutes past 4
Explanation
Introduction / Context:The original stem said “straight line,” but the options match known right-angle times. Applying the right-angle condition |30H − 5.5M| = 90 with H between 4 and 5 yields two solutions within the hour, one of which lies between 4:30 and 5:00.
Given Data / Assumptions (Recovery Applied):
- Interpretation repaired to “right angle.”
- Hour H = 4; minutes M in (30, 60).
- Equation: |120 − 5.5M| = 90.
Concept / Approach:Solving yields M = 21 9/11 and M = 54 6/11. Only 54 6/11 is between 4:30 and 5:00.
Step-by-Step Solution:
120 − 5.5M = 90 ⇒ M = 21 9/11 (not in window).120 − 5.5M = −90 ⇒ 5.5M = 210 ⇒ M = 54 6/11 (in window).Verification / Alternative check:Substitute M = 54 6/11; angle equals 90° exactly.
Why Other Options Are Wrong:50, 42, 46 minutes are not exact right-angle solutions from the formula.
Common Pitfalls:Forgetting that the hour hand moves (0.5 deg per minute), hence 5.5M term.
Final Answer:54 6/11 minutes past 4