4. (15 points) Two heaters are connected sequentially to the same DC power source. The water in the pot boiled after $t_{1}=3$ minutes from the first heater. The same water, taken at the same initial temperature, boiled after $t_{2}=6$ minutes from the second heater. How long would it take for the water to boil if the heaters were connected in parallel? Neglect heat dissipation to the surroundings.
Answer: 2 min.

Solution. The amount of heat required for heating in the first case $Q=I^{2} R_{1} t_{1}$. The amount of heat required for heating in the second case $Q=$ $I^{2} R_{2} t_{2}$. The amount of heat required for heating in the case of parallel connection $Q=I^{2} \frac{R_{1} \cdot R_{2}}{R_{1}+R_{2}} t$. As a result, we get:

$$
t=\frac{t_{1} t_{2}}{t_{1}+t_{2}}=\frac{3 \cdot 6}{3+6}=2 \text { min. }
$$