4. (10 points) The distance between places $A$ and $B$ is 600 kilometers. Two people, Jia and Yi, start cycling from $A$ to $B$ at the same time. Jia rides 40 kilometers per day, while Yi rides 60 kilometers per day but rests every other day. At the end of the $\qquad$th day, the distance Yi has left to $B$ is twice the distance Jia has left to $B$.
【Analysis】This problem can be set up by assuming that at the end of the $x$-th day, the distance from $B$ to Yi is twice the distance from $B$ to Jia. According to the problem, on the $x$-th day, Jia has traveled $40 x$, and is still ( $600-40 x$ ) kilometers away from $B$, while Yi has traveled $60 \div 2 \times x$, and is still ( $600-60 \div 2 \times x$ ) kilometers away from $B$. Based on the condition that "the distance from $B$ to Yi is twice the distance from $B$ to Jia," we can set up the equation $600-60 \div 2 \times x=2 \times(600-40 x)$, and solve it accordingly.

【Solution】Solution: Let the $x$-th day be the day when the distance from $B$ to Yi is twice the distance from $B$ to Jia, we get:
$$
\begin{aligned}
600-60 \div 2 \times x & =2 \times(600-40 x) \\
600-30 x & =1200-80 x \\
50 x & =600 \\
x & =12
\end{aligned}
$$

Answer: On the 12th day, the distance from $B$ to Yi is twice the distance from $B$ to Jia. Therefore, the answer is: 12.