$Pb9.$ A plate and frame filter having $1\mathrm{.}5m^2$ surface area, where filtering occurs, is being operated at a constant pressure. In feed $10\%$ solid, having specific gravity $3,$is mixed in water. During filtration incompressible cake is formed.

$($a$)$ Compute the time required to wash the cake formed at the end of $90$ minutes of filtering at the same pressure using $5m^3$ of water.

$\backslash$table$[[$Time $(s),V,m^3$