2018 AMC 8
Complete problem set with solutions and individual problem pages
The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say noon. When he is done shopping, his watch says and his car clock says . Later that day, Sri loses his watch. He looks at his car clock and it says . What is the actual time?
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Solution 1
We see that every minutes the clock passes, the watch passes minutes. That means that the clock is as fast the watch, so we can set up proportions. . Cross-multiplying we get . Now, this is obviously redundant, because we could just eyeball it to see that the watch would have passed hours. But this method is better when the numbers are a bit more complex, which makes it both easier and reliable. Either way, our answer is .
Solution 2
The ratio of the car clock to the watch clock is a ratio of 35:30 or 7:6 due to the clock being ahead by 5 minutes after 30 minutes has passed. This means that when the car clock passes hours, the watch has passed hours, meaning that the time would be .
