1983 TYS

Two variables $x$ and $t$ are connected by the differential equation $\frac{\text{d}x}{\text{d}t}=\frac{kx}{10-x}$, where $0 < x < 10$ where $k$ is a constant. It is given that $x=1$ when $t=0$ and that $x=2$ when $t=1$. Find the value of $t$ when $x=5$, giving your answer to three significant figures.