Finding rate constants for parallel reactions
By some simple mathematics, you can reach the following equations (the first of which you have reached):

$[X]=[X]_0\cdot e^{-(k_1+k_2)t}$

$[Y]=\frac{k_1}{k_1+k_2}[X]_0\cdot e^{-k_1 t}$

$[Z]=\frac{k_2}{k_1+k_2}[X]_0\cdot e^{-k_2 t}$

The $1:3$ ratio that you have arrived at is correct,  i.e. $\dfrac{k_1}{k_2}=\dfrac{1}{3}$.

Substituting this in the equation for $\ce{X}$, we get

$[X]=[X]_0\cdot e^{-4k_1 t}$

All that is left to do now is to substitute and solve, which leads to the answer:

$(k_1,k_2)\equiv(0.015\ (min)^{-1},0.045\ (min)^{-1})$

There you go!

PS: I've used $[X]_0$ for representing the initial concentration of $\ce{X}$.