<Question>
Jim and Martha are standing together at the corner of a rectangular field. Jim walks diagonally across the field. Martha gets to the same location by walking along its length and width. The field is 300 feet wide and 400 feet long. How many feet less than Martha does Jim walk?
</Question>

<think>
<Plan_1>
Okay, let's see. So the problem is about Jim and Martha walking to the same location in a rectangular field. The field is 300 feet wide and 400 feet long. Jim walks diagonally across the field, while Martha walks along the length and the width. We need to find out how many feet less Jim walks compared to Martha.

First, I need to visualize the field. It's a rectangle, right?

<prompt_1.1> Visualize the problem using the above plan. </prompt_1.1>
</Plan_1>

<Execution_1>
<execution_1.1>
The width is 300 feet, and the length is 400 feet. So if they start at the corner, Jim is taking the diagonal path from one corner to the opposite corner. Martha is walking along two sides: either the length and the width. Since the field is rectangular, the sides are the length and the width. So Martha's path would be the sum of the length and the width. Wait, but does she walk along both the length and the width, or just one of them? The problem says she gets to the same location by walking along its length and width. So I think that means she walks the entire length and then the entire width, or vice versa. So her total distance would be the length plus the width. Let me confirm that.
</execution_1.1>
</Execution_1>

<Plan_2>
Based on execution_1.1:
So, Martha's distance is 300 feet + 400 feet.

<prompt_2.1> Calculate Martha's walking distance using the above plan. </prompt_2.1>

Now, Jim walks diagonally across the field. The diagonal of a rectangle can be found using the Pythagorean theorem, which is a^2 + b^2 = c^2, where a and b are the sides, and c is the diagonal. So here, the width and length are the two sides, so the diagonal would be sqrt(300^2 + 400^2).

<prompt_2.2> Calculate Jim's walking distance using the above plan. </prompt_2.2>
-----

Wait, that seems straightforward, but let me make sure I didn't miss anything. Is there a possibility that Martha walks along the diagonal instead of the two sides? But the problem says she walks along the length and width, so she must be taking the two sides. Jim takes the diagonal. So the difference is 700 - 500 = 200 feet.
</Plan_2>

<Execution_2>
<execution_2.1>
That adds up to 700 feet. 

On the other hand, Jim walks the diagonal. To find the length of the diagonal, we use the Pythagorean theorem. Let me write that out. The diagonal d is sqrt(300^2 + 400^2). Let me calculate that. 

First, 300 squared is 90,000, and 400 squared is 160,000. Adding those together gives 90,000 + 160,000 = 250,000. Then the square root of 250,000 is 500. So Jim walks 500 feet.
</execution_2.1>

<execution_2.2>
Let me calculate that.

First, 300 squared is 90,000, and 400 squared is 160,000. Adding those together gives 90,000 + 160,000 = 250,000. Then the square root of 250,000 is 500. So Jim walks 500 feet.
</execution_2.2>
</Execution_2>

<Plan_3>
Based on execution_2.1, execution_2.2:
Therefore, Martha walks 700 feet, Jim walks 500 feet.
The difference is 700 - 500 = 200 feet.

Wait, that seems correct, but let me double-check. The field is 300 feet by 400 feet. The diagonal is indeed 500 feet because 3-4-5 triangles are common Pythagorean triples.

<prompt_3.1> Verify the calculations using the above plan. </prompt_3.1>
-----

Another way to think about it: the total distance Martha walks is the perimeter path from one corner to the opposite corner, which is two sides, while Jim takes the shortest path, the diagonal. 

Another check: if the field were a square, say 100 feet on each side, the diagonal would be 100√2 ≈ 141.4 feet, which is less than 200 feet (100+100).
So in this case, the diagonal is 500, which is less than 700.
So the difference is 200 feet.

I think that's solid.
The answer is 200 feet.

**Final Answer**
</Plan_3>

<Execution_3>
<execution_3.1>
So scaling up, 300 and 400 would give a diagonal of 500, since 300 is 3*100, 400 is 4*100, and 5*100 is 500. That checks out.
</execution_3.1>
</Execution_3>

<Final_answer>
Therefore, Jim walks $700 - 500 = \boxed{200}$ feet less than Martha.
</Final_answer>
</think>