1. **State the problem:** We have the relationship between pressure $P$, volume $V$, and temperature $T$ given by the formula $$PV = T.$$ We know the rates of change of $P$ and $V$ and want to find the rate of change of $T$ when $P=150$, $V=5$, $\frac{dP}{dt}=20$, and $\frac{dV}{dt}=-0.1$. 2. **Formula and rules:** Differentiate both sides of the equation $$PV = T$$ with respect to time $t$ using the product rule: $$\frac{d}{dt}(PV) = \frac{dT}{dt}$$ $$P \frac{dV}{dt} + V \frac{dP}{dt} = \frac{dT}{dt}$$ 3. **Substitute known values:** $$P = 150, \quad V = 5, \quad \frac{dP}{dt} = 20, \quad \frac{dV}{dt} = -0.1$$ 4. **Calculate:** $$\frac{dT}{dt} = 150 \times (-0.1) + 5 \times 20 = -15 + 100 = 85$$ 5. **Interpretation:** The temperature is increasing at a rate of 85 K/s. **Final answer:** $\boxed{85}$ K/s