In this paper, we study the (distinct) positive integer solution of the equation
\begin{equation*}\label{eq12}\frac{k}{n} = \frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_t}\end{equation*} with $n>k\geq 2$ and $ t\geq 2$.
We show that the above equation has at least one distinct positive integer solution if it has a positive integer solution.
When $k=5$, we show the above equation has at least one distinct positive integer solution for all $n\geq 3$
except possibly when $n\equiv 1, 5041, 6301, 8821, 13861, 15121(\mbox{mod } 16380)$ with $t=3$,
and for all $n\geq 3$ except possibly when $n\equiv 1, 81901(\mbox{mod } 163800)$ with $t=4$.
Furthermore, we point out that the above equation has at least one distinct positive integer solution for all $n(>k)$
when $t\geq k\geq 2$.
