1. Two sisters were picking currants: the elder one in a four-liter bucket, and the younger one in a bucket with a capacity of 3.5 liters. The elder sister always worked faster than the younger one. When the elder sister had collected three quarters of her bucket, and the younger one had collected more than half of hers, the girls switched buckets. Continuing to work at the same speed as before the switch, they finished their work simultaneously. How many times faster did the elder sister pick berries compared to the younger one?
Solution: $0.75 \cdot 4=3$ liters of berries were collected by the older sister by the time they exchanged buckets. Let x liters be the amount collected by the younger sister by this time. Since the work rate of the sisters is the same before and after exchanging buckets, we can set up the equation: $\frac{3}{x}=\frac{3.5-x}{1} ; 3=x(3.5-x)$. The roots of the equation are $x_{1}=2 ; x_{2}=1.5$

The second root does not fit the problem's condition, as the younger sister had collected more than half of her bucket by the time of the exchange. Substituting $\mathrm{x}=2$ into the proportion, we get that the older sister worked 1.5 times faster than the younger one.

Answer: 1.5.