In four years, Rose will be twice the age of Anne. Two years ago, Annewas one-third the age of Rose. How old are they now?

Let's denote Rose's current age as R and Anne's current age as A.

From the problem, we have two equations:

1. In four years, Rose will be twice the age of Anne. This can be written as: R + 4 = 2 * (A + 4).

2. Two years ago, Anne was one-third the age of Rose. This can be written as: A - 2 = 1/3 * (R - 2).

Now we can solve these two equations.

First, simplify the first equation: R + 4 = 2A + 8, which simplifies to R = 2A + 4.

Substitute R from the first equation into the second equation: 2A + 4 - 2 = 1/3 * ((2A + 4) - 2), which simplifies to 2A + 2 = 2/3A + 2/3.

Solving this equation gives A = 6.

Substitute A = 6 into the first equation: R = 2 * 6 + 4, which gives R = 16.

So, Rose is 16 years old and Anne is 6 years old.