jmc

There are $4\frac{1}{2}$ hours from 7:30 a.m. to noon, and $4$ hours from noon to 4 p.m., meaning Walter was away from home for a total of $8\frac{1}{2}$ hours, or $8.5\times 60=510$ minutes. Tallying up the times he was not on the bus, he has $6\times 50=300$ minutes in classes, $30$ minutes at lunch, and $2\times 60=120$ minutes of "additional time". That is a total of $300+30+120=450$ minutes that Walter was away from home, but not on the bus. Therefore, Walter spent $510-450=60$ minutes on the bus, and the answer is $\boxed{60}$