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.