$\begin{array}{c}6 \cdot 78 \text { Let } f(x)=|x-p|+|x-15|+|x-p-15| \text {, where } \\ 0<p<15 \text {. Find the minimum value of } f(x) \text { for } x \text { in the interval } p \leqslant x \leqslant 15. \end{array}$