3. The Field of Wonders in the Land of Fools has the shape of a rectangle with sides of 6 km and 2.5 km. Malvina and Buratino started moving towards each other from two of its non-adjacent vertices along the diagonal at speeds of 4 km/h and 6 km/h, respectively. At the same moment, the poodle Artemon started running at a speed of 12 km/h from Malvina to Buratino, then, upon reaching him, instantly turned around and ran back to Malvina, and so on. What distance will Artemon cover while the fairy-tale characters are meeting?
Answer: 7.8 km. Solution. The diagonal of the rectangle is $\sqrt{6^{2}+2.5^{2}}=\sqrt{36+\frac{25}{4}}$ $=\sqrt{\frac{169}{4}}=\frac{13}{2}$ (km). Therefore, Malvina and Pinocchio will meet after $\frac{13}{2}:(4+6)$ $=\frac{13}{2 \cdot 10}=\frac{13}{20}$ (hour). During this time, the poodle Artemon ran at a speed of 12 km/h. Thus, he ran a distance of $\frac{13}{20} \cdot 12=\frac{78}{10}($ km $)$.