Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of $10$ miles per hour. Jack walks to the pool at a constant speed of $4$ miles per hour. How many minutes before Jack does Jill arrive?
$\textbf{(A) }5\qquad\textbf{(B) }6\qquad\textbf{(C) }8\qquad\textbf{(D) }9\qquad \textbf{(E) }10$
Using $d=rt$, we can set up an equation for when Jill arrives at the swimming pool:
$1=10t$
Solving for $t$, we get that Jill gets to the pool in $\frac{1}{10}$ of an hour, which is $6$ minutes.  Doing the same for Jack, we get that 
Jack arrives at the pool in $\frac{1}{4}$ of an hour, which in turn is $15$ minutes.  Thus, Jill has to wait $15-6=\boxed{\textbf{(D)}~9}$
minutes for Jack to arrive at the pool.