After having collected samples along the shore all day long, a marine biologist walks back to her campsite, 3.02 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 understand the pattern of the dog's movement.
Let's call the speed of the marine biologist x km/h. Since the dog runs twice as fast, its speed would be 2x km/h.
Now, let's analyze the dog's movement. The dog runs from the campsite to meet the scientist and then turns around to run back to the campsite. This means the dog covers the same distance twice.
So, we can break down the dog's movement into two parts:
1. The distance the dog runs from the campsite to meet the scientist.
2. The distance the dog runs from the meeting point back to the campsite.
Let's calculate each of these distances:
1. Distance from campsite to the meeting point:
The marine biologist walks a total distance of 3.02 km, and the dog runs at twice the speed of the marine biologist. Therefore, the dog covers this distance in half the time. So, the distance the dog runs from the campsite to the meeting point is (3.02 km) * (2/3) = 2.013 km.
2. Distance from the meeting point back to the campsite:
The dog now turns around and runs at the same speed back to the campsite. Since the total distance from the campsite to the meeting point and back is 3.02 km, this distance is 3.02 km - 2.013 km = 1.007 km.
Now, to find the total distance the dog runs, we need to add up the distances from the two parts of its movement: 2.013 km + 1.007 km = 3.02 km.
Therefore, the dog runs a total distance of 3.02 km.