A planned development is to have a $50$ m x $40$ m asphalt$-$covered parking lot. Local drainage regulations require a

minimum slope of $0\mathrm{.}4\%$ toward drainage inlets, a minimum time of concentration of $5$ min for each inlet, and that the

kinematic wave equation be used to calculate the actual time of concentration. For asphalt, n $=0\mathrm{.}012.$ The standard

grate inlet in the jurisdiction has dimensions of $406$ mm $\backslash$times $711$ mm$,$ and the IDF function and where i and ie are in mm$/$h$,$ t and tc are in minutes, and L is in meters. $($a$)$ Determine the number of grate inlets required

in the parking lot, and sketch their locations such that each grate has the same catchment area. $($b$)$ How many grate

inlets would be required if each inlet were depressed by $1$ inch $(25$ mm$)?$ Sketch their locations such that each grate has

the same catchment area. $[$Hint: For both cases, assume the minimum time of concentration and then verify this

assumption after design.$]$where i and ie are in mm$/$h$,$ t and tc are in minutes, and L is in meters. $($a$)$ Determine the number of grate inlets required

in the parking lot, and sketch their locations such that each grate has the same catchment area. $($b$)$ How many grate

inlets would be required if each inlet were depressed by $1$ inch $(25$ mm$)?$ Sketch their locations such that each grate has

the same catchment area. $[$Hint: For both cases, assume the minimum time of concentration and then verify this

assumption after design.$]$