Final answer:
The total distance between home and school is 3/4 of a mile, as 1/4 of a mile is 1/3 of the way to school.
Step-by-step explanation:
The student has walked 1/4 of a mile, which is equivalent to 1/3 of the distance to school. To find the total distance between home and school, we set up a proportion. Since 1/4 mile represents 1/3 of the total distance, we can write the equation:
1/4 mile = 1/3 (total distance)
To solve for the total distance, we can multiply both sides of the equation by 3 (the reciprocal of 1/3):
3 * (1/4 mile) = total distance
3/4 mile = total distance
Thus, the total distance between home and school is 3/4 of a mile.