Question 1032285
The DE {{{dT/dt=k(T-38) }}} becomes {{{dT/(T-38) = kdt}}}.

==> ln(T-38) = kt + c.

T(0) = 75 ==> ln37 = c.  ==> {{{ln((T-38)/37) = kt}}}.

Now T(30) = 60 ==> {{{ln((60-38)/37) = 30k}}}, or  {{{(1/30)ln(22/37) = k}}}.

==> {{{ln((T-38)/37) = (1/30)ln(22/37)t}}}, or {{{ln((T-38)/37) = ln(22/37)^(t/30)}}}

==> {{{(T-38)/37 = (22/37)^(t/30)}}}, or 

{{{T = 38+37*(22/37)^(t/30)}}}.  

To solve for t when T = 55, plug 55 for T into the last equation.
I will leave the final calculation to you, and you should manage to get {{{highlight(t = 45)}}} minutes, to the nearest minute.