Kirchoff's laws and electrical circuit

Question

Two batteries with emf ε1 = 10 V and emf ε2 = 20 V and internal resistances r1 = 1 Ω and r2 = 2 Ω, respectively, are connected in parallel, and then connected in parallel to a resistor of R = 30 Ω resistance (see diagram).

1. Write down as many Kirchhoff equations as to calculate all the currents flowing in each part of the circuit.
2. Calculate those currents.
3. Calculate the power dissipated in each of the batteries (P1 and P2, respectively) and in the resistor (P3).

Answer 1

I will give you some hints.

For each battery, internal resistance is in series with the battery.

There will be 3 currents, so you need 3 equations.

The first follows from KCL, while the other two from KVL