DK-GEORGMOHR 1994

A train travels a certain distance at a constant speed. Whose speed is increased by $10$ kilometers per hour, the trip can be made $40$ minutes faster. If, on the other hand, the speed is reduced by $10$ kilometers per hour, the trip takes $1$ hour further. How long is the distance traveled?

The third-degree polynomial $P(x)=x^3+2x^2-3x-5$ has the three roots $a$ , $b$ and $c$ . State a third degree polynomial with roots $\frac{1}{a}$ , $\frac{1}{b}$ and $\frac{1}{c}$ .

In a right-angled triangle in which all side lengths are integers, one has a cathetus length $1994$ . Determine the length of the hypotenuse.