My friend found two old watches. He wound them, set them, and started both of them at the same time. He placed the two old watches on one wrist and his new watch on the other wrist. Forty-five minutes later one of the old watches had gained 1 minuate and the other old watch lost 2 minutes. The next morning one watch read 7:00 and the other read 6:00. At what time did he start the two old watches?

Question

My friend found two old watches. He wound them, set them, and started both of them at the same time. He placed the two old watches on one wrist and his new watch on the other wrist. Forty-five minutes later one of the old watches had gained 1 minuate and the other old watch lost 2 minutes. The next morning one watch read 7:00 and the other read 6:00. At what time did he start the two old watches?

I need a good explanation on how to solve this problem. Thanks

Answer 1

To solve this problem, we can break it down into steps:

Step 1: Understand the problem
In this problem, we need to determine at what time the two old watches were started. We are given that both watches were wound, set, and started at the same time. After 45 minutes, one watch gained 1 minute, and the other lost 2 minutes. The next morning, one watch read 7:00 and the other read 6:00. We need to find the starting time of the two old watches.

Step 2: Analyze the given information
From the given information, we know that one watch gained 1 minute, and the other watch lost 2 minutes in 45 minutes. So, the difference between the two watches is 3 minutes after 45 minutes.

Step 3: Determine the time it takes for one watch to gain 1 minute.
Since one watch gained 3 minutes over 45 minutes, we can calculate the time it takes for the watch to gain 1 minute by dividing 45 minutes by 3 minutes. This gives us 15 minutes for each minute gained.

Step 4: Determine the starting time for the watch that reads 7:00
Since the watch that reads 7:00 gained 1 minute and it takes 15 minutes to gain 1 minute, we can subtract 15 minutes from the current time to find the starting time. Substracting 15 minutes from 7:00 gives us 6:45.

Step 5: Determine the starting time for the watch that reads 6:00
Since the watch that reads 6:00 lost 2 minutes and it takes 15 minutes to gain 1 minute, we can subtract 30 minutes from the current time to find the starting time. Subtracting 30 minutes from 6:00 gives us 5:30.

Step 6: Determine the time at which the two old watches were started
From step 4 and step 5, we have found that the watch that reads 7:00 was started at 6:45, and the watch that reads 6:00 was started at 5:30. Therefore, he started the two old watches at 5:30.

So, the answer to the problem is that he started the two old watches at 5:30.