Final answer:
The question is a mathematical problem about calculating the total number of rungs in a ladder based on described movements. The middle rung is determined to be the starting point for Kathy, with her subsequent movements factored in to find the total. The ladder has 17 rungs in total.
Step-by-step explanation:
The student's homework question involves a series of movements on a ladder and requires calculating the total number of rungs on the ladder based on those movements. Kathy's actions on the ladder are described step by step: she initially stands on the middle rung, climbs 3 rungs, moves 5 rungs (which could be up or down, but since she continues climbing afterwards, we assume she moved down), climbs up 6 rungs, and finally climbs the remaining 3 rungs to the top.
To determine the total number of rungs on the ladder, we add all of Kathy's movements together. Starting from the middle rung, she climbs up 3 rungs, moves down 5 rungs, climbs up 6 rungs, and finally ascends the last 3 rungs to the top. Since Kathy ends at the top of the ladder after these movements, we can determine that the middle rung where she started is actually the 6th rung (because she moves down 5 rungs to climb up 6 rungs after).
In total, Kathy climbs 3 + 6 + 3 = 12 rungs to go from the middle to the top. Since the middle rung is the 6th rung, there are 5 rungs below her starting point. Adding the lower and upper halves of the ladder, we get 5 + 12 = 17 rungs in the entire ladder. Therefore, the correct answer is (a) 17.