You are the proud new pup-parent of a brand new puppy! When you bring the pup for his first check-up, the vet explains to you that it's a common misconception that dogs age 7 "dog years" for every human year. Instead, he says, small breed dogs age 15 "dog years" in the first year, 9 "dog years" in the second year, and 4 "dog years" per year after that.
You wonder, when will my pup and I be the same age?
Let's say I am currently 18.

One year and a half, approximately.

Step-by-step explanation:

At time t=0, we have a puppy of 0 years and you are 18.

The first year of the puppy is equivalent to 15 dog years, so he will be 15 and you 19.

The second year, he adds 9 dog years. He became 24 dog-years the second year. You will be 20 years old.

He will age 4 dog-years from now, so you will never reach him and have the same age from then.

You have the same age in between the end of the first year and the end of the second year. Probably at the half of the second year (one year and a half from birth).

both equations and proportions are better.