Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?
$\text{(A)}\ 48 \qquad \text{(B)}\ 51 \qquad \text{(C)}\ 52 \qquad \text{(D)}\ 54 \qquad \text{(E)}\ 55$
Shea has grown $20\%$, if x was her original height, then $1.2x = 60$, so she was originally $\frac{60}{1.2}=50$ inches tall which is a $60 - 50 = 10$ inch increase.  Ara also started off at $50$ inches.  Since Ara grew half as much as Shea, Ara grew $\frac{10}{2} = 5$ inches.  Therefore, Ara is now $50+5=55$ inches tall which is choice $\boxed{E}.$