5.4. Postman Pechkin delivers mail by bicycle to four villages: Prostokvashino, Smetanino, Tvorozhnoye, and Molochnoye (see figure). He knows that the distance from Prostokvashino to Tvorozhnoye is 9 km, from Prostokvashino to Smetanino is 13 km, from Tvorozhnoye to Smetanino is 8 km, and from Tvorozhnoye to Molochnoye is 14 km. Find the distance from Prostokvashino to Molochnoye.

![](https://cdn.mathpix.com/cropped/2024_05_06_3ededfe9bc358e4d64a4g-2.jpg?height=406&width=714&top_left_y=266&top_left_x=721)
Answer: 19 km.

Solution. The distance from Prostokvashino to Smetanino with a detour to Tvorozhnoye is $9+8=17$ (km), and without the detour - 13 km. Therefore, the detour to Tvorozhnoye (from the highway and back) is 4 km. The distance from Prostokvashino to Molochnoye with a detour to Tvorozhnoye is $9+14=23$ (km), and without the detour: $23-4=19$ (km).

You can also introduce variables and set up equations.

## Grading Criteria:

+ correct answer and correct solution provided

$\pm$ correct and justified reasoning provided, but one arithmetic error is made

干 all necessary equations are correctly set up, but not solved

干 only the correct answer is provided

- incorrect solution provided