4. If one white and two black cows graze all the grass on the meadow in 5 weeks, and three white and four black cows graze all the grass on the meadow in 2 weeks, how many weeks will it take for one black cow to graze all the grass on the meadow? Assume that cows of the same color graze at the same rate, that the initial amount of grass on the meadow is always the same, and that the grass on the meadow grows at a fixed rate until it is completely eaten.
4. Answer: 20 weeks. Let $a$ be the initial amount of grass on the meadow, and $b$ the amount of grass that grows during one week. Let $p$ and $q$ be, respectively, the amount of grass that one white and one black cow graze during one week. The conditions of the problem can now be translated into the equations $a+5 b=5(p+2 q)$ and $a+2 b=2(3 p+4 q)$. From the first equation, we get $p=\frac{a+5 b-10 q}{5}$, and substituting this into the second equation gives $a+2 b=6 \cdot \frac{a+5 b-10 q}{5}+8 q$, which simplifies to $5 a+10 b=6 a+30 b-20 q$, or $a+20 b=20 q$. However, this means that the amount of grass available on the meadow over 20 weeks is exactly sufficient for one black cow to graze for 20 weeks, thus solving the problem.