Answer:
EMF = 11.35 V
R = 0.031Ω
Step-by-step explanation:
To find the battery's EMF and the internal resistance we need to use Ohm's law:

Where:
V: is the voltage
I: is the current
R is the resistance
We have:
The current through the battery is 64.2 A and the potential difference across the battery terminals is 9.36 V:
(1)
When only the car's lights are used, the current through the battery is 1.96 A and the terminal potential difference is 11.3 V:
(2)
By solving equation (1) and (2) for R we have:


Hence, the internal resistance is 0.031 Ω.
Now, by entering R into equation (1) we can find the battery's EMF:


Therefore, the battery's EMF is 11.35 V.
I hope it helps you!