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Cassandra's Watch

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January 4, 2009

Problem Statement

Cassandra sets her watch to the correct time at noon. At the actual time of 1:  ⁣ 00 PM \text{1: \!\,00 PM}, she notices that her watch reads 12:  ⁣ 57 \text{12: \!\,57} and 36 36 seconds. Assuming that her watch loses time at a constant rate, what will be the actual time when her watch first reads 10:  ⁣ 00 PM \text{10: \!\,00 PM}? <spanclass=′latex−bold′>(A)</span> 10:  ⁣ 22 PM and 24 seconds<spanclass=′latex−bold′>(B)</span> 10:  ⁣ 24 PM<spanclass=′latex−bold′>(C)</span> 10:  ⁣ 25 PM <span class='latex-bold'>(A)</span>\ \text{10: \!\,22 PM and 24 seconds} \qquad<span class='latex-bold'>(B)</span>\ \text{10: \!\,24 PM}\qquad<span class='latex-bold'>(C)</span>\ \text{10: \!\,25 PM} <spanclass=′latex−bold′>(D)</span> 10:  ⁣ 27 PM<spanclass=′latex−bold′>(E)</span> 10:  ⁣ 30 PM <span class='latex-bold'>(D)</span>\ \text{10: \!\,27 PM}\qquad<span class='latex-bold'>(E)</span>\ \text{10: \!\,30 PM}
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