As Olivia is driving her car on a long straight road, she spots Sophia cycling in the same direction $\frac{3}{4}$ mile in front of her. After she passes her, she can see her in her rear mirror until she is $\frac{3}{4}$ mile behind her. Olivia drives at a constant rate of 16 miles per hour, and Sophia cycles at a constant rate of 10 miles per hour. For how many minutes can Olivia see Sophia?