2018 AMC 8 Problems/Problem 12
Contents
Problem
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 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?
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 .
--BakedPotato66 --Rishi09
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 when the watch time has been 30 minutes since the "start time". This means that when the car clock passes hours, the watch has passed hours, meaning that the time would be .
~edited by SHREYU.MEDATATI
Solution 3
From 12:00 pm (noon) to 7:00 pm, the car clock has passed 12 35-minute cycles (12 X 35 = 420) because 7 hours = 420 minutes. So, 12 30-minute cycles (12 X 30 = 360) for the watch time are 360 minutes, which is 6 hours. Therefore, 6 hours added to 12:00 pm (noon) makes the answer .
~SaxStreak
Solution 4 (a version of solution 3)
7 hours have passed since 12:00 pm and 7 hours = 420 minutes because there are 60 minutes in an hour. Because every 35 minutes, the clock is ahead by 5 minutes, you need to divide 420 by 35 to find out how many times it happens. 420 divided by 35 is 12. Then you would multiply 12 by 5 because the clock is ahead by 5 minutes. 12 times 5 is 60, so that means that the clock is ahead by 60 minutes. In order to find the watch's time, you must find what was 60 minutes earlier than 7:00 which is .
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See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
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Followed by Problem 13 | |
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