your mistake is treating r as a constant ... it's not.
I arrived at 54.663 min, but hear this ... this problem has some ugly constants.
when t = 0 , h = 3 ...
when t = 45 , h = 1.5
solve for k
I'll leave you to work out the rest ... like I said C and k are two ugly constants. I stored their values in my calculator and found that h = 0 at about t = 55 min.