After throwing their sleeping bags into the backseat of their car, they...................more than 400 miles to reach their destination.

"Driving" is the present participle form of the verb, which does not fit the past context set by the rest of the sentence. The sentence requires a simple past tense verb to describe a completed action rather than an ongoing or present action.

"Having driven" is a perfect participle phrase that suggests a completed action prior to another past action. However, it is unnecessarily complex for this sentence structure and does not match the straightforward narrative of simply stating what they did after throwing their sleeping bags into the car.

"Had driven" is the past perfect tense, used to indicate an action that was completed before another past action. While grammatically correct, it implies a sequence that is not required in this context, making it more complicated than necessary for the sentence's meaning.