Chapter 18 - The Laws of Thermodynamics - Problems and Conceptual Exercises - Page 646: 53

$4.5\times 10^2K,5.0\times 10^2K$

We know that $\eta=1-\frac{T_c}{T_h}$ We plug in the known values to obtain: $0.11=1-\frac{T_c}{T_c+55}$ $\implies\frac{T_c}{T_c+55}=0.89$ $0.89T_c+48.95=T_c$ This simplifies to: $T_c=445K=4.5\times 10^2K$ $\implies T_h=T_c+55=445+55=500K=5.0\times 10^2K$