1. Calculate how many pages Bob has read by the time Jane starts.
- Bob starts at 4:30 pm.
- Jane starts at 5:20 pm.
- Time Bob reads alone $=5: 20 \mathrm{pm}-4: 30 \mathrm{pm}=50$ minutes.
- Bob's reading rate $=30$ pages per hour.
- Convert Bob's rate to pages per minute: 30 pages $/ 60$ minutes $=0.5$ pages per minute.
- Pages Bob reads in 50 minutes $=0.5$ pages $/$ minute $* 50$ minutes $=25$ pages.

So, at 5:20 pm, Bob is on page 25. Jane is on page 0 .
2. Set up equations to find when they will be on the same page.

Let $t$ be the number of minutes after 5:20 pm.
- Bob's page number at time $t$ :

Bob starts at page 25 at 5:20 pm.
Bob's reading rate $=0.5$ pages $/$ minute .
Bob's page at time $t=25+0.5 t$
- Jane's page number at time $t$ :

Jane starts at page 0 at 5:20 pm.
Jane's reading rate $=40$ pages per hour.
Convert Jane's rate to pages per minute: 40 pages $/ 60$ minutes $=4 / 6$ pages per minute $=$ 2/3 pages per minute.
Jane's page at time $t=0+(2 / 3) t=(2 / 3) t$

3. Set their page numbers equal to each other to find $t$.

$$
\(\begin{aligned}
& 25+0.5 t=(2 / 3) t \\
& 25+(1 / 2) t=(2 / 3) t
\end{aligned}\)
$$


To solve for $t$, get all $t$ terms on one side:

$$
\(25=(2 / 3) t-(1 / 2) t\)
$$


Find a common denominator for the fractions (which is 6 ):

$$
\(\begin{aligned}
& 25=(4 / 6) t-(3 / 6) t \\
& 25=(1 / 6) t
\end{aligned}\)
$$


Multiply both sides by 6 :

$$
\(\begin{aligned}
& t=25 \times 6 \\
& t=150 \text { minutes }
\end{aligned}\)
$$

4. Convert the time to hours and minutes (optional, but good for understanding).

150 minutes $=2$ hours and 30 minutes.

So, they will start reading the same page 150 minutes after 5:20 pm.
The final answer is 150 .