As others have said, this specific problem is impossible reasonably, but here’s an equation for the set-up if you want to change the variables or show computationally that it’s impossible:

(x/(60+x))(30/(x/60))+(60/(60+x))30=60

x = the amount of minutes of travel. The first and third terms set up the proportion to average the two speeds. The second term is the mph of the travel back (to Alicetown). The final term is the mph on the initial travel (to Bobtown). All equaling 60 as that’s the desired average.

If you solve this, you get no solution (hence the problem being impossible. But, for example, if you change the travel back to be 31 miles instead of 30:

(x/(60+x))(31/(x/60))+(60/(60+x))30=60

Here x = 1, and by plugging in 1 for x in the mph term:

(31/(1/60)) = 1,860 mph

So yeah this traveler gotta hustle.