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A typical batch filtration cycle consists of filtration followed by washing. One such filtration unit operating at constant pressure difference first filters a slurry during which $5$ liters of filtrate is collected in $\:100 s$. This is followed by washing, which is done for $t_{W}$ seconds and uses $1$ liter of wash water. Assume the following relation to be applicable between the applied pressure drop ${\Delta P}$, cake thickness $L$ at time $t$, and volume of liquid $V$ collected in time $t$:
 
$$\frac{\Delta P}{L}=k_{1}\frac{dV}{dt}\:\:;\:\:L=k_{2}V,\:if \:   L   \:is\:changing.$$

$k_{1}$ and $k_{2}$ can be taken to be constant during filtration and washing. The wash time $t_{W}$, in seconds (up to one decimal place), is ________.
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