How Far Does a Bookworm Travel Through a 3-Volume Set?

[soroban]

There is a 3-volume set of books
$\quad$on a bookshelf in the usual manner.

Each volume has two covers, each $\frac{1}{4}$ inch thick,
$\quad$and the printed portion is $1$ inch thick.

A bookworm starts at the first page of Volume 1
$\quad$and eats his way to the last page of Volume 3.

How far does the bookworm travel?

Before you ask: we want his shortest distance.)
.

 

[Evgeny.Makarov]

Spoiler

View attachment 3731
The distance is $d$.

 

[soroban]

Hello, Evgeny.Makarov!

Absolutely correct!

If you have not seen the problem before,
. . good work!

Even if you had seen this problem before,
. . thank you for participating.