Suppose it exists, and q is on BC, p is on DC, QP is perpendicular to DC, and auxiliary line DM is perpendicular to BC. Then the triangle QPC is similar to the triangle DMC. Then, QC:DC=PC:MC, which means 5t: 10=( 14-4t):8. The answer is seven quarters. Q is on BC because 7 quarters are less than 12/5, and P is on DC because 7 quarters are more than 1 and less than 14 quarters. So the hypothesis holds. So it exists.