Let's break down the problem to find out how many inches the bookworm eats through.

Key information:

• There are 25 volumes, each 2 inches thick.
• Each volume has a front cover and a back cover, each of which is $\frac{1}{4}$ inch thick.
• The bookworm starts inside the front cover of the first volume and ends after eating through the back cover of the last volume.

Step-by-step solution:

1. Understanding the bookworm’s path:

   • The bookworm starts inside the front cover of the first volume, which means it doesn’t eat through the first front cover.
   • It stops after it eats through the back cover of the last volume, which means it doesn’t eat through the last back cover either.

2. What the bookworm eats through:

   • The bookworm eats through all the volumes except for the first front cover and the last back cover.
   • For all other parts of the encyclopedia, it eats through the entire thickness of each volume, including the covers.

3. Calculating the distance covered:

   • The total thickness of the 25 volumes:
     $25 \, \text{volumes} \times 2 \, \text{inches/volume} = 50 \, \text{inches}$
   • However, since the bookworm doesn’t eat the front cover of the first volume and the back cover of the last volume, we subtract their thickness: $50 \, \text{inches} - \left(\frac{1}{4} \, \text{inch} + \frac{1}{4} \, \text{inch}\right) = 50 \, \text{inches} - \frac{1}{2} \, \text{inch} = 49.5 \, \text{inches}$

Conclusion:

The bookworm eats through 49.5 inches of the encyclopedia.

Would you like further explanation on any step?

Here are 5 related questions to consider:

1. How would the solution change if the bookworm started at the back cover of the first volume instead?
2. What if each cover was $\frac{1}{2}$ inch thick instead of $\frac{1}{4}$?
3. How would the answer differ if there were 30 volumes in the encyclopedia?
4. Can you calculate how many inches the bookworm eats if the front and back covers are $\frac{1}{8}$ inch thick?
5. How many inches would the bookworm eat if it started at the front cover of the first volume and ate through to the front cover of the last volume?

Tip: Always subtract the portions of the object that the problem specifies as not being eaten or traveled through to avoid overestimations.