Question

gaming in a role - playing video game, the user navigates his or her character across an unknown land using a map. on the map, the distance between the characters home and the health food store is 2 centimeters, the distance between the health food store and the first dungeon is 3 centimeters, and the distance between the first dungeon and the characters home is 7 centimeters. if the actual distance between the health food store and the first dungeon is 4 kilometers, how far will the character have to travel in the game to visit all three destinations and return to their starting point?

Explanation:

Step1: Find the scale factor

Let the scale factor be $k$. We know that on - map distance between health food store and first dungeon is 8 cm and actual distance is 4 km = 400000 cm. So $k=\frac{400000}{8}=50000$.

Step2: Find actual distances of other segments

The on - map distance between character's home and health food store is 2 cm. Actual distance $d_1 = 2\times50000=100000$ cm = 1 km.
The on - map distance between first dungeon and character's home is 7 cm. Actual distance $d_2 = 7\times50000 = 350000$ cm = 3.5 km.

Step3: Calculate total distance for round - trip

The total one - way distance to visit all three destinations is $1 + 4+3.5=8.5$ km.
The total round - trip distance is $2\times8.5 = 17$ km.

Answer:

17