2018 AMC 8 Problems/Problem 12

Problem 12

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

We see that every 35 minutes the clock passes, the watch passes 30 minutes. That means that the clock is times faster than the watch, so when the car clock passes 7 hours, the watch has passed 6 hours, meaning that the time would be