Two old watches were found. Both watches were set for the current time. Forty-five minutes later one old watch was 1 minute ahead and the other old watch was 2 minutes behind. The next morning one watch read 7am and the other read 6am. At what time were the two old watches set?
To solve this problem, let's break it down step by step.
1. We know that initially, both watches were set for the current time, which we can assume is the same time for both watches.
2. Forty-five minutes later, one watch was 1 minute ahead and the other was 2 minutes behind. This means that the time difference between the watches has changed by 3 minutes (1 minute + 2 minutes = 3 minutes).
3. From the given information, we can deduce that the time difference between the two watches is changing by 3 minutes every 45 minutes.
4. Now let's analyze the time difference between the watches on the next morning. One watch reads 7am, and the other reads 6am. The time difference between these two is 1 hour (which is equal to 60 minutes). Therefore, during the night, the time difference between the two watches increased by 60 minutes.
5. We can conclude that the watches take 45 minutes to change the time difference by 3 minutes and that it takes 60 minutes to change the time difference by 60 minutes.
6. To determine the original setting time, we can set up an algebraic equation.
Let's assume that the original time was x minutes (since it is the same for both watches).
According to the given information, we can write the following equation:
x + (45/3) + (60/60)x = 45
Simplifying the equation:
x + 15 + x = 45
2x + 15 = 45
2x = 30
x = 15
Therefore, the original setting time for both watches was 15 minutes.