Mountaineer

An Austrian mountaineer left Zurglatt, his village, at eight o'clock in the morning, and started his climb towards the refuge Tirpitz, on Gross Glossen mountain. He walked at a steady pace, without stopping, and his increase in heart pulse rate was negligible. He reached the refuge at three in the afternoon, i.e. seven hours since he left the village. At the refuge he rested, admired the view, scribbled some notes on his diary, sang three lieder, ate two sausages and drank a litre of beer. He then slipped into his sleeping bag and fell asleep.

The next morning, at eight o'clock, he started his descent, again with a steady pace, but faster, since he was travelling downhill. He reached Zurglatt at one in the afternoon, after walking for five hours.

Could there be a point along the path where the mountaineer walked, on the outbound and the return journey, exactly at the same time of day?

Solution