To find out how far the dog has to run to catch up with the cat, we need to compare the distances covered by both animals.
For every 7 meters the dog runs, the cat runs 4 meters. This gives us a ratio of 7:4.
Let's calculate how many sets of 7 meters the dog needs to run to match the cat's distance:
12 m รท 7 m = 1.714 sets of 7 meters.
Since we cannot have a fraction of a set, we will consider the next whole number, which is 2.
Now, we multiply the number of sets (2) by the distance covered in each set (7 m), to find out how far the dog needs to run to catch up with the cat:
2 sets * 7 meters per set = 14 meters.
Therefore, the dog needs to run 14 meters to catch up with the cat.