A classical mechanics problem by Panchajanya Das

The only important statement in the question that you have to identify is, “The speed of the bug is 1m/s throughout”. This is the core. Once you identify that it’s speed was constant throughout, the actual path the bug took becomes irrelevant. No matter how complicated that path was, the total distance would be still given by the simple equation “distance = speed x time”.

“Bug is traveling at a constant speed of 1 m/s throughout it’s motion. At this constant speed, he travels for 1 hour. So distance = speed x time = 1 m/s x 3600s = 3600meter.”

There is a great anecdote about John von Neumann, dealing with essentially this same problem. From wikipedia :

Lothar Wolfgang Nordheim described von Neumann as the "fastest mind I ever met",[154] and Jacob Bronowski wrote "He was the cleverest man I ever knew, without exception. He was a genius."[161] George Pólya, whose lectures at ETH Zürich von Neumann attended as a student, said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."[162] Halmos recounts a story told by Nicholas Metropolis, concerning the speed of von Neumann's calculations, when somebody asked von Neumann to solve the famous fly puzzle:[163]

Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann, "All I did was sum the geometric series."[16]