Rita is four years younger than five times Cara's age.Cara is half the age of Nathan.Nathan's age is half that of Peter's.Collectively, the children's ages equal twenty.How old is Peter?

Let's denote the ages of the children as follows:

• Rita = R
• Cara = C
• Nathan = N
• Peter = P

From the problem, we have the following equations:

1. R = 5C - 4 (Rita is four years younger than five times Cara's age)
2. C = N/2 (Cara is half the age of Nathan)
3. N = P/2 (Nathan's age is half that of Peter's)
4. R + C + N + P = 20 (Collectively, the children's ages equal twenty)

We can substitute equations 1, 2, and 3 into equation 4 to solve for the ages:

Substitute R from equation 1 into equation 4: 5C - 4 + C + N + P = 20

Substitute C from equation 2 into the new equation: 5(N/2) - 4 + N/2 + N + P = 20 5N/2 - 4 + N/2 + N + P = 20 4N + P = 24

Substitute N from equation 3 into the new equation: 4(P/2) + P = 24 2P + P = 24 3P = 24

Solve for P: P = 24 / 3 P = 8

So, Peter is 8 years old.