Q$3.(15$ points$)$ The rainfall intensities during each $20-$min of a $120-$min storm over a $400-$acre

basin are $2\mathrm{.}5,3,1\mathrm{.}2,6,4\mathrm{.}2$ and $2\mathrm{.}2$ inches $\frac{?}{hr},$ respectively. The direct runoff from the basin is $85$

acre$-$ft$.$ Determine the $$ index $($in in$/$hr$)$ for the basin.