Exponential and Poisson Distribution Problem

#1
Hello all, we have this problem.

Suppose that the continuous random variable T has the Exponential distribution with expected value 4. Given that T = t, for any t > 0, the discrete random variable S has the Poisson distribution with expected value 3t.
Find:
a) E(S)
b) Var(S)

Can you help me out with this one? I struggle to find the answer, but i know its relatively easy .. Thank you.
 
#3
We know that T~Expo(λ) => Ε(Τ) = 1/λ so we can derive that λ = 1/4
We also know that S~Poi(λ) => λ here is the expected value, so λ = 3t = 3T

Somewhere here i get stuck..