a dog starts chasing a cat when they are 12 meters. for every 7 meters that the dog runs, the cat runs 4 meters. how far does the dog have to run to catch up with the cat?

Question

a dog starts chasing a cat when they are 12 meters. for every 7 meters that the dog runs, the cat runs 4 meters. how far does the dog have to run to catch up with the cat?

Answer 1

Let the distance run by the dog be 7x m

let the distance run by the cat be 4x m

so 7x = 4x + 12
3x = 12
x = 4

So the dog has to run 7(4) or 28 m to catch the cat.

check:
In the same time that the dog ran 28 m , the cat ran
16 m
but the cat had a 12 m head-start , giving us also 16+12 or 28 m

Answer 2

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 ÷ 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.

Answer 3

To find out how far the dog has to run to catch up with the cat, we need to calculate how much distance the cat has covered when the dog catches up. Let's assume the dog runs x meters to catch up with the cat.

The dog runs 7 meters for every 4 meters the cat runs. Therefore, the ratio of the distances traveled by the dog and the cat is 7:4.

We can create a proportion to find the distance the cat has covered when the dog catches up:

12 meters (initial distance) + x meters (distance the dog has to run) : x meters (distance the dog has to run) = 7 meters (distance the dog runs per 4 meters run by the cat) : 4 meters (distance the cat runs)

By cross-multiplying, we get:
(12 + x) * 4 = 7 * x

Expanding the equation, we have:
48 + 4x = 7x

Simplifying the equation by subtracting 4x from both sides, we get:
48 = 3x

Dividing both sides by 3, we find:
x = 16

Therefore, the dog has to run 16 meters to catch up with the cat.