1. Ivan Ivanovich approached a source with two empty cans; one held 10 liters, and the other held 8 liters. Water from the source flowed in two streams - one stronger, the other weaker. Ivan Ivanovich simultaneously placed the cans under the streams and, when half of the smaller can was filled, he switched the cans. To Ivan Ivanovich's surprise, the cans filled up simultaneously. How many times more water does the stronger stream provide compared to the weaker one?
Solution: Let x liters of water fill the larger can while 4 liters fill the smaller can. After the switch, (10-x) liters fill the larger can while 4 liters again fill the smaller can. Since the flow rates are constant, the ratio of the volumes of water filled in the same time is also constant. We can set up the equation: $\frac{4}{x}=\frac{10-x}{4} ; x^{2}-10 x+16=0$, which has two roots $x_{1}=2, x_{2}=8$. The two roots of the equation correspond to two possibilities: placing the smaller can under the stronger or the weaker stream first. However, in both cases, the answer is the same: one stream provides twice as much water as the other.

Answer: 2.