Questions: Kathy stood on the middle rung of a ladder She climbed up 3 rungs, moved down 4 rungs, and then climbed up 6 rungs Then she climbed up the remaining 3 rungs to the fop of the ladder. How many rungs are there in the whole ladder?

Kathy stood on the middle rung of a ladder She climbed up 3 rungs, moved down 4 rungs, and then climbed up 6 rungs Then she climbed up the remaining 3 rungs to the fop of the ladder. How many rungs are there in the whole ladder?

Transcript text: Kathy stood on the middle rung of a ladder She climbed up 3 rungs, moved down 4 rungs, and then climbed up 6 rungs Then she climbed up the remaining 3 rungs to the fop of the ladder. How many rungs are there in the whole ladder?

Solution

Solution Steps

Step 1: Calculate Total Movement (TM)

To find the total movement from the initial position, sum all upward and downward movements along with the final climb. Mathematically, it's represented as $TM = \sum U_i + \sum (-D_i) + FC$. Given upward movements [3, 6], downward movements [4], and final climb 3, we calculate $TM = 9 + (4) + 3 = 16.$

Step 2: Determine Total Rungs (TR)

Since the individual starts from the middle rung, the total movement from the middle to the top, multiplied by 2, gives the total number of rungs on the ladder. Therefore, $TR = 2 \times TM = 2 \times 16 = 32.$

Final Answer:

The total number of rungs on the ladder is 32.

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