2 watches are set at 9 AM one watch runs 2 minutes fast each hour and another runs 1 minute slow each hour. The faster watch will be a hour ahead and blank AM the next morning.
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she said 5 am
5 AM
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9AM to 5AM is 20 hours.
the slow watch will be 20 minutes behind
the fast watch will be 40 minutes ahead
To find out how many hours the faster watch will be ahead and the time it would be the next morning, we need to calculate the time difference between the two watches for each hour.
Let's analyze the situation step by step:
1. Difference per hour for the faster watch: The faster watch runs 2 minutes fast each hour. Since there are 60 minutes in an hour, the watch will be 2/60 = 1/30 hour ahead per hour.
2. Difference per hour for the slower watch: The slower watch runs 1 minute slow each hour. Similarly, it will be 1/60 hour behind per hour.
3. Now, let's calculate the total time difference between the two watches:
- After the first hour, the faster watch gains 1/30 hour, while the slower watch loses 1/60 hour.
- So, in one hour, the faster watch gains (1/30) - (1/60) = 1/60 hour.
4. To determine when the faster watch will be 1 hour ahead, we need to find out how many hours it takes to accumulate a time difference of 1 hour.
- Since the faster watch gains 1/60 hour per hour, it will take 1/(1/60) = 60 hours to gain 1 hour.
5. Next, we need to calculate the time the next morning when the faster watch is 1 hour ahead.
- If the initial time is 9 AM, and the faster watch takes 60 hours to gain 1 hour, it will be 9 AM + 60 hours = 9 AM + 2,400 minutes = 11 AM the next morning.
Therefore, the faster watch will be 1 hour ahead and show 11 AM the next morning.