It is said that the philosopher Immanuel Kant was a man of exceptionally regular habits. He particularly liked to have his grandfather clock set at exactly the right time. One day he was distressed to find that his clock had run down. Evidently his manservant had forgotten to wind it. Kant restarted the clock but couldn’t reset the hands because his watch was at the repair shop and he had no way of knowing the correct time.
That evening he walked over to the house of his friend Meyer, a mile or so away, for their weekly chess game. Kant always walked at the same steady pace, though he had never taken note of how long this journey took him. He glanced at the grandfather clock as he was leaving and noted his arrival time on the clock in Meyer’s hallway. He played several games of chess, then returned home. He walked along the same route by which he had come, with the same regular gait that had not changed for years. He had no idea how long his trip took. When he arrived home, he immediately set his grandfather clock correctly.
From the information in this story, can you figure out the procedure Kant used so that he could set his clock correctly on returning home?
Kant noted his departure time on Meyer’s clock and figured out how long the chess games had taken. When he arrived home, he looked at the grandfather clock to see the total elapsed time of his trip. From the total elapsed time, he subtracted the amount of time he had spent in Meyer’s house, divided the difference (his total walking time) by 2, and added the length of his return walk to the time he left Meyer’s house. The result was the correct time of his arrival home, and that’s the time he set on his clock.