A certain slow clock loses 15 mins every hour. Suppose the clock is set to the correct time at 9 AM. What will the correct time be when the slow clock first shows 10 AM? Show your work.

Also, does to lose an hour mean to go forward or fall back an hour?

losing time means running too slow

when an hour has passed, the clock has only moved 45 min
it is running at 3/4 speed (45/60)

so when it shows an hour has passed,
an hour and 20 min (4/3 hr) has actually passed

the correct time is...10:20 AM

very cool

Well, if the slow clock loses 15 minutes every hour, then for every hour that passes, it will actually show only 45 minutes. So, after the first hour, when the slow clock shows 10 AM, in reality, only 45 minutes will have passed.

Now, let's calculate how many intervals of 45 minutes it takes to reach 10 AM. To do this, we can set up an equation:

45 minutes * X intervals = 60 minutes

Simplifying the equation, we have:

45X = 60

Dividing both sides by 45, we get:

X ≈ 1.333

So, it takes approximately 1.333 intervals of 45 minutes to reach 10 AM.

Now, let's convert this to hours. Since we started at 9 AM, we need to add the time it takes for 1.333 intervals of 45 minutes:

9 AM + 1 hour (for the full hour) + 0.333 hours (for the remaining 45 minutes)

0.333 hours is equivalent to 20 minutes (approximately).

So, when the slow clock first shows 10 AM, the correct time will be approximately 9:20 AM.

Now, to answer your second question, losing an hour means moving the clock forward. For example, during daylight saving time, we "lose" an hour by setting the clock forward by one hour. So, technically, we're losing an hour of sleep but gaining more sunlight in the evening. Time can be quite the trickster, I must say!

To find the correct time when the slow clock first shows 10 AM, we need to determine how many minutes have elapsed in the slow clock from 9 AM to 10 AM.

Given that the slow clock loses 15 minutes every hour, we can calculate the number of minutes lost in one hour:

15 minutes/hour

Since we want to find how many minutes have been lost from 9 AM to 10 AM, we can multiply the number of hours (from 9 AM to 10 AM) by the number of minutes lost per hour:

1 hour * 15 minutes/hour = 15 minutes

Therefore, by the time the slow clock shows 10 AM, it has lost 15 minutes. Now, we need to subtract these lost minutes from 10 AM to find the correct time:

10 AM - 15 minutes = 9:45 AM

So, the correct time will be 9:45 AM when the slow clock first shows 10 AM.

Regarding your second question, "to lose an hour" typically refers to the act of setting the clock back by one hour. This is commonly done during daylight saving time when clocks are adjusted to give more daylight in the evenings.

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