Question

I have a grandfather clock. it runs slightly fast, gaining one second every four hours. it needs winding once a week, which i do just before noon every saturday. the clock has to be stopped to carry out this process, and after it has been restarted it is always 15 seconds slow at precisely 12 o’clock. today is thursday and the correct time now is 8 pm. how many seconds past 8 o’clock does the clock show

Answer 1

The grandfather clock is 17 seconds ahead at 8 PM on Thursday, as it gains time since last wound with an initial deficit when winding.

Step-by-step explanation:

The grandfather clock in question gains one second every four hours. Since it's only Thursday at 8 PM and the clock is wound on Saturday just before noon, we need to calculate how much time has passed since last wound. From Saturday to Thursday, there are five days, plus another eight hours on Thursday itself.

The first step is to calculate the total gain in seconds from Saturday to Thursday 8 PM. In each hour, the clock gains 1/4 of a second, so in one day (24 hours) it will gain 24 * (1/4) = 6 seconds. Over five days, this gain will be 5 * 6 = 30 seconds.

For the additional 8 hours on Thursday, the clock gains 8 * (1/4) = 2 seconds. Therefore, the total gain by 8 PM Thursday is the five-day gain plus the eight-hour gain, which equals 30 + 2 = 32 seconds.

However, each week when the clock is wound, it starts 15 seconds slow. As it was last wound five days plus eight hours ago, we need to add this initial deficit to the total gain. Therefore, the clock will be 15 seconds slow plus 32 seconds gained, which equals a total of 17 seconds ahead.

Therefore, at 8 PM on Thursday, the grandfather clock shows 8 PM and 17 seconds.