6. A uniformly growing uniform grassland is divided into two unequal parts, $\mathrm{A}$ and $\mathrm{B}$. A herd of cows first eats the grass on plot A, finishing it in exactly 7 days. Then the herd continues to eat the grass on plot B at the same speed, finishing it in 4 days, at which point plot A has just recovered to the state it was in when the cows started eating. What is the simplest integer ratio of the area of plot A to plot B? $\qquad$
【Answer】105:44
【Analysis】A The grassland from being eaten clean to growing back to the original amount of grass takes 4 days. Assuming A grassland grows 1 unit of grass per day, then in 4 days it grows 4 units. The original amount of grass in A grassland is 4 units. The speed at which the cow eats grass is $(4+7) \div 7=\frac{11}{7}$ (units); the cow eats $\frac{11}{7} \times 4=\frac{44}{7}$ units of grass in 4 days on B grassland; assuming B grassland grows $\mathrm{x}$ units per day, with an original amount of grass of $4 \mathrm{x}$ units, then the equation is $4 \mathrm{x}+(7+4) \mathrm{x}=\frac{44}{7} ; x=\frac{44}{105}$; the ratio of the grass growth rates, which is the ratio of the grassland areas, is 1: $\frac{44}{105}=105: 44$