A normal clock loses 3 minutes per hr and another clock gains 5 min per hr. How many hours after from now, both the clocks will show the correct time simultaneously?
What is the starting point?
To find out how many hours it will take for both clocks to show the correct time simultaneously, we need to determine the time difference between the clocks' rates.
The first clock loses 3 minutes per hour, which means it falls 3 minutes behind the correct time every hour.
The second clock gains 5 minutes per hour, which means it advances 5 minutes ahead of the correct time every hour.
To determine the cumulative difference between the clocks, we add the rates of both clocks: 3 minutes per hour (loss) + 5 minutes per hour (gain) = 8 minutes per hour.
Since the clocks have a difference of 8 minutes per hour, it will take 8 minutes for them to be completely synchronized.
Knowing that there are 60 minutes in an hour, we can set up a proportion to find the number of hours it will take for both clocks to show the correct time:
8 minutes is to 60 minutes as x hours is to 1 hour.
8/60 = x/1
Cross-multiplying: 8 = 60x
Dividing both sides by 60: x = 8/60
Thus, it will take 8/60 or 2/15 hours for both clocks to show the correct time simultaneously.
To solve this problem, we need to find the time it takes for the two clocks to have the same time, given that one clock loses 3 minutes per hour (let's call this Clock A) and the other clock gains 5 minutes per hour (let's call this Clock B).
Let's assume the current time is T hours. After T hours, Clock A will be behind by 3 minutes per hour, so it will be behind by 3T minutes. Similarly, Clock B will be ahead by 5T minutes.
To find the time when the clocks show the correct time simultaneously, we need the time when the time difference between the two clocks is 0. In other words, we need to find the value of T that makes the equation (5T - 3T) = 0 true.
Simplifying the equation, we have:
5T - 3T = 0
2T = 0
T = 0
This means that the two clocks will show the correct time simultaneously at the current time. Therefore, no additional hours need to pass for the clocks to be in sync.