A Student ratio from two independent samples

Let $X_1,X_2,…,X_{10}$ be a random sample from the $N(3,4)$ distribution and let $Y_1,Y_2,…,Y_{15}$ be a random sample from the $N(-3,6)$ distribution. Assume that the two samples are drawn independently. Define $\bar X=\frac1{10}\sum_{i=1}^{10}X_i$, $\bar Y=\frac1{15}\sum_{j=1}^{15}Y_j$, and $S=\sqrt{\frac19\sum_{i=1}^{10}(X_i-\bar X)^2}$. Then the distribution of $U=\dfrac{\sqrt{5}(\bar X+\bar Y)}{S}$ is