As Liam is riding his bicycle on a long straight road, he spots Noah jogging in the same direction $\frac{1}{4}$ mile in front of him. After he passes him, he can see him in his rear mirror until he is $\frac{1}{4}$ mile behind him. Liam rides at a constant rate of 10 miles per hour, and Noah jogs at a constant rate of 7 miles per hour. For how many minutes can Liam see Noah?