Solution: The Speed of Spiders Math Puzzle

The spider will never reach the top of the wall. Each step of the way, it covers half the remaining distance to the top, so there is always some distance to go. In the next step only half of the previous distance is traveled, still leaving a bit more to cover. This is true for both versions of the puzzle.

But, there is a concept in mathematics of a "limit." This is a number or point that is approached, even if it is never reached. We can say that as the number of steps the spider travels approaches infinity, the distance traveled approaches the height of the wall as a limit. If the spider took an infinite number of steps, it would reach the top.

Now with that perspective, there is a difference between the two versions. If each step takes an hour, then it would take an infinite number of steps to reach the top in an infinite amount of time. But in Version 2 each step takes half as long as the previous step. The total time to reach the top approaches two hours as a limit.