In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase. Suppose that it takes you one hour to stroll at a constant speed up one spiral of this staircase, which has a radius of 18 feet and a height of 48 feet and makes 6 revolutions.

(a) Assuming the spiral staircase is centered about the $z$-axis, find a vector parametric equation for the helical path you take from the point $(18,0,0)$ to the point $(18,0,48)$ that makes $6$ revolutions during the time interval $0 \leq t \leq 1$.

$\boldsymbol{\vec{r}}(t) =$

(b) How far did you walk?

feet