How long for DC to respond to 'admit with explanation'?

I parked at a meter that would become free at 9:00PM and when i parked it was 8:45PM. By the time i could break change, blah blah blah it was 8:55PM and i figured since its free after 9:00PM theres no point in walking back. While i was gone, i was issued a ticket at 8:49PM. I admitted the ticket with an explanation by mail the day after i got the ticket.



How long does it normally take for me to get a response back stating whether the ticket stands or is reduced?How long for DC to respond to 'admit with explanation'?
It appears to me that someoone saw you leave the car and then issued the ticket, which is bull$hit, and they should be fired. In another 11 minutes you would not have to put any money in to begin with.

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