At 1pm Henry leaves his house and heads north to the river. He arrives at 4.30pm. At the same time, his brother joe leaves their house and heads south to the desert and arrives at 3:30pm. If they both traveled at the same speed and the distance between the river and the desert is 360 miles, what was their rate of travel?

Let's first determine the travel times for both Henry and Joe.

Henry leaves his house at 1:00 PM and arrives at the river at 4:30 PM. The time taken by Henry is:

4:30 PM - 1:00 PM = 3 hours and 30 minutes = 3.5 hours.

Joe leaves at the same time (1:00 PM) and arrives at the desert at 3:30 PM. The time taken by Joe is:

3:30 PM - 1:00 PM = 2 hours and 30 minutes = 2.5 hours.

Now, since we know the total distance between the river and the desert is 360 miles, we can set up the equation based on their equal speeds.

Let \( r \) be the rate of travel (in miles per hour) for both of them. The distance traveled by Henry can be represented as:

\[
\text{Distance by Henry} = r \times 3.5
\]

The distance traveled by Joe can be represented as:

\[
\text{Distance by Joe} = r \times 2.5
\]

Since the total distance between the river and the desert is 360 miles, we can write:

\[
\text{Distance by Henry} + \text{Distance by Joe} = 360
\]

Substituting the distances gives:

\[
r \times 3.5 + r \times 2.5 = 360
\]

Combining like terms:

\[
r(3.5 + 2.5) = 360
\]

This simplifies to:

\[
r(6) = 360
\]

Now, solving for \( r \):

\[
r = \frac{360}{6} = 60
\]

Thus, the rate of travel for both Henry and Joe is:

\[
\boxed{60} \text{ miles per hour.}
\]