Final answer:
The car's headlights left on will last approximately 15 hours, as calculated by using the battery capacity in watt-hours (1200 Wh) and the total power consumption of the headlights (80 W).
Step-by-step explanation:
The question pertains to how long the headlights will last on a parked car with the headlights left on. We can calculate this by first understanding the power usage of the headlights and the capacity of the car battery. The power usage for two headlights can be determined by adding the power of each headlight, which is 40 W for one headlight. Hence, the total power usage is 40 W + 40 W = 80 W. Since the car's battery is rated at 100 Ah (ampere-hours), we need to convert this capacity into watt-hours by multiplying by the voltage, which is 12 V. Therefore, the battery capacity is 12 V × 100 Ah = 1200 Wh (watt-hours).
Considering the total power usage of the headlights is 80 W, we can now estimate how long they will last by dividing the total battery capacity by the power usage. The number of hours the headlights will last is 1200 Wh ÷ 80 W = 15 hours. Therefore, the driver concludes that the headlights will shine for approximately 15 hours before the battery is fully discharged.