Wristwatch Tower

If you think you’re a whiz, can you solve this puzzle?

There is a man who lives on the top of a hill. He stays alone and has only an old grandfather clock in his house which tells him the time. Every day he winds the clock, else the clock will stop. One day he forgets and wakes up to see the clock has stopped at some point of time at night. Now he needs to go downhill to the village square and see the correct time in the Village Clock Tower (in this idyllic village, no one has a wristwatch, and everyone relies on the Clock tower for the time)

He has a horse which takes a fixed time to go downhill (say x) and a fixed time to go uphill (say y). Going uphill obviously takes longer (i.e y>x). However, the man does not know the value of x and y.

The question is: How will he adjust the time on his grandfather clock to the correct time?

(with the assumption that grand pa’s clock is too heavy to carry to the village & no wrist watch meaning he has no tool to monitor the time goes)
It could not be done, no matter how many times he go forth and back and write down the time. I have tried seriously calculated every possible means.
the best he could do is:
1. go to the the village and buy another well-adjusted clock to adjust the one at home. (this clock could be used as a mean to adjust the grand pa’s clock in the future.)
2. go to the village and memorize the position of the sun. the next day he could adjust the clock’s hands with the sun’s position (but then it won’t be precise).
or
3. He could go to the village,
write down what time it is,
go home to his house and go back to the village,
count the time lapsed (that’s the x + y, or the time needed to go and come back house-village-house).
write down what time it is when he left the village for the second time.
Adjust the grand pa’s clock with ‘That last recorded time’ + ‘the time lapsed or (x+y)’.

That will make the grand pa’s clock to show = ‘the correct time’ + x

-> note that when he get home for the last time, his recorded time is already late y minutes for his trip back from the village to his house.
but because he added ‘the lapse time’ (x + y) then it is =
correct-time – y + (x + y), and he get ‘correct-time + x’

SO, from that time on, if he has to be at the village by 5 o’clock, he should leave at least when the grand pa’s clock show 5 o’clock because his clock is now x minutes early than the village’s tower clock.

thank you.

Tower clockmaker in the Philippines