Apuppy and a kitten are 180 meters apart when they see each other. the puppy can run at a speed of 25 m/sec, while the kitten can run at a speed of 20 m/sec.
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how soon will the kitten catch the puppy if the kitten starts running after the puppy?

P=25t and k=180+20t

The puppy will catch the kitten when p=k so we can say:

25t=180+20t  subtract 20t from both sides

5t=180  divide both sides by 5

t=36

So the puppy would catch the kitten after 36 seconds.

Now if you really meant what you typed, "How soon will the kitten catch the puppy if the kitten starts running after the puppy?"  The kitten would never catch the puppy as the puppy is faster and the equations would become:

p=180+25t, k=20t, trying to set p=k would give you:

20t=180+25t, subtract 25 t from both sides

-5t=180  divide both sides by -5

t=-36

Time cannot be negative as we are trying to solve for how long "after" the cat starts running, so there is no solution.  (as stated earlier, the puppy is faster than the kitten by 5m/s so each second that passes the puppy and kitten would get 5 meters further apart instead of ever getting closer together)

Dbecause there are negatives surrounding ding it