To find the number of miles Janice walked, we need to divide the total time she walked (7/8 hour) by the time it takes her to walk 1 mile (1/4 hour).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(7/8 hour)/(1/4 hour) = (7/8 hour) * (4/1 hour)
We can simplify this expression by canceling out the common factor of hours:
= (7/2) * 4
= 14 * 2
= <<14*2=28>>28 miles
So, Janice walked 28 miles. Answer: \boxed{28}.