In triangle XYZ, X_1, Y_1, and Z_1 are the midpoints of $\overline{YZ},$ $\overline{XZ},$ and $\overline{XY},$ respectively. A dilation maps $X$ to $Y$ with scale factor 3. A second dilation maps $Y$ to $Z_1$ with scale factor 5. When both dilations are combined, what is the overall scale factor?