A rain storm$|$lasting for four hours was recorded at three gauges $($A$,$ B$,$ C$)$ within a catchment of $500k{m}^2.$

The rainfall hyetographs recorded at each gauge are presented in Table Q$1\mathrm{.}1.$ The $10$mm$,1$ hour unit

hydrograph for the catchment is shown in Table Q$1\mathrm{.}2.$

Table Q$1\mathrm{.}1$

Table Q$1\mathrm{.}2$

$($i$)$ Determine the rainfall hyetograph for the entire catchment if the areas obtained from Thiessen

polygons are $200k{m}^2$ and $120k{m}^2$ for gauges A and $B$ respectively.

$($ii$)$ If losses are a constant $5m\frac{m}{h}r$ throughout the storm, determine the hydrograph of the quick

response runoff.