After having collected samples along the shore all day long, a marine biologist walks back to her campsite, 2.12 km away. Her dog runs ahead, at twice the speed, reaches the campground and turns around until it meets her again. Then, the dog proceeds to run back to the campground again. This continues until the marine biologist reaches her campground. What distance did the dog run?

To find the distance the dog ran, we need to determine how many times the dog ran back and forth between the marine biologist and the campground.

Let's consider the distance traveled by the marine biologist in one round trip between the shore and the campground. She walks 2.12 km from the shore to the campground and 2.12 km back to the shore, which results in a total distance of 4.24 km per round trip.

Since the dog runs at twice the speed of the marine biologist, it covers the entire distance in half the time. Therefore, for each round trip of the marine biologist, the dog completes two round trips between the campground and the marine biologist.

Therefore, the distance the dog runs is equal to the distance covered by the dog in one round trip multiplied by the number of round trips the dog completes before the marine biologist reaches the campground.

To find the number of round trips, we divide the distance traveled by the marine biologist (2.12 km) by the distance traveled by the dog in one round trip (4.24 km). This gives us:

Number of round trips = 2.12 km / 4.24 km = 0.5 round trips

Since the dog completes two round trips for each round trip of the marine biologist, we multiply the number of round trips by 2:

Number of dog's round trips = 0.5 round trips * 2 = 1 round trip

Therefore, the dog runs the distance covered in one round trip, which is 4.24 km.

So, the dog runs a total distance of 4.24 km.