To proceed with the calculations, let's assume you've measured the length of the trip on the map to be 1 inch. Given the scale where $\frac{1}{4}$ inch equals 100 miles, here's how you can calculate the total distance:

Step-by-Step Calculation:

1. Understand the Scale:

   • $\frac{1}{4}$ inch on the map represents 100 miles.

2. Set Up the Proportion:

   • You measured 1 inch on the map. We want to find the number of miles this corresponds to.

   $\text{Distance in miles} = \text{Measured Length in inches} \times \left(\frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}}\right)$

3. Perform the Calculation:

   • Plug in 1 inch for the measured length:

   $\text{Distance in miles} = 1 \text{ inch} \times \left(\frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}}\right)$

   • Simplify the fraction $\frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}}$:

   $\frac{100 \text{ miles}}{\frac{1}{4} \text{ inch}} = 100 \text{ miles} \times 4 = 400 \text{ miles}$

   • Thus, 1 inch on the map corresponds to 400 miles.

Final Answer:

If the length of the trip on the map is 1 inch, the actual distance represented by that length would be 400 miles.

Do you have any other questions or need further details? Here are some follow-up questions to consider:

1. What if the measured length were 2 inches? How would the distance change?
2. How can you verify that your measurement and calculation are correct?
3. How would you handle a different map scale, such as $\frac{1}{8}$ inch equals 100 miles?
4. Could you convert the final distance from miles to kilometers?
5. What tools would you use to ensure accurate measurements on the map?

Tip: Always keep a calculator handy for scale conversions, especially when dealing with fractions and large distances!