A dog starts chasing a cat when they are 12 meters apart. For every 7 meters that the dog runs, the cat runs 4 meters. How far does the dog have to run to catch up to the cat?
The cat runs 4/7 as fast as the dog. So, if the dog has to run x meters, the cat will have run 4/7 x during that time.
x = 12 + 4/7 x
3/7 x = 12
x = 28
That is, the cat will have run 16 meters while the dog runs 28 meters, having made up the cat's 12-meter head start.
It can’t because by the time the dog reaches the cats position the cat is further away and when the dog reaches that location the cat is even further away and the sequence repeats
Well, the situation seems quite "ruff"! Let's do some calculations to see if we can help our furry friends out.
For every 7 meters the dog runs, the cat runs 4 meters. That means the dog is gaining 3 meters on the cat every time they both run that distance.
Since the initial distance between them is 12 meters, we need to determine how many times the dog needs to run 7 meters to catch up to the cat.
12 divided by 3 gives us 4. So, the dog needs to run 7 meters, four times to catch up to the cat.
4 multiplied by 7 meters equals 28 meters. Therefore, the dog has to run 28 meters to catch up to the cat.
So, the final answer is "the dog has to run 28 meters to reach the cat." I hope they both enjoy the chase!
To find out how far the dog has to run to catch up to the cat, we need to find the distance at which they are equal.
Let's analyze the situation step by step:
1. Distance covered by the dog = x
2. Distance covered by the cat = (x + 12) since they start 12 meters apart.
According to the given information, for every 7 meters that the dog runs, the cat runs 4 meters. So we can set up a proportion to compare their distances:
Distance covered by the dog / Distance covered by the cat = 7 / 4
Substituting the variables, we get:
x / (x + 12) = 7 / 4
To solve for x, we can cross-multiply:
4x = 7(x + 12)
Now, we can solve for x:
4x = 7x + 84
Subtracting 7x from both sides:
-3x = 84
Dividing by -3:
x = -28
However, since distance cannot be negative, we discard this solution.
From the equation, we can see that the dog will never catch up to the cat since the ratio of their speeds is fixed (7:4) and the cat starts 12 meters ahead. The dog would have to run indefinitely to catch up to the cat, but will never actually reach it.
Idk what Steve said
You have to make a model like:
. ----------------
. |. Dog | cat |
. ----------------
. |. 7 | 4. |
. |. 14. | 8. |
. |. 21. |. 12. |
. |. 28. | 16. |
. |. 35 | 20. |
|. (42).| 24. |
. |. | 38 |
. | | (42).|
Guys try to ignore the dots
.