Question

claude is spending his vacation in the city and planning what he will do the first day. looking at a map, he plans to start at his hotel. from there, he will go to the fine - arts museum, and then to the sculpture garden. he will walk between each location. on the map, the distance between the hotel and the fine - arts museum is 0.9 inches. the distance between the fine - arts museum and the sculpture garden is 1.1 inches. on the map scale, 1 in. represents 3 km. enter the scale. 1 in. : 3 km map city 1 in. km enter the actual distance, m, from the hotel to the museum. 2.7 kilometers enter the actual distance, g, from the museum to the garden. 1 kilometers i want to do this optional task to determine the actual distance, m. write a proportion using the variable m. then solve for m using means and extremes. map city in. km i want to do this optional task to determine the actual distance, g. write a proportion using the variable g. then solve for g using means and extremes.

Explanation:

Step1: Set up the proportion

The map - scale is 1 in. : 3 km. Let the map - distance be $d_{m}$ (in inches) and the actual distance be $d_{a}$ (in km). The proportion is $\frac{d_{m}}{d_{a}}=\frac{1}{3}$.

Step2: Find the actual distance from hotel to museum

Given $d_{m}=0.9$ in. Substitute into the proportion $\frac{0.9}{m}=\frac{1}{3}$. Cross - multiply: $m = 0.9\times3=2.7$ km.

Step3: Find the actual distance from museum to sculpture garden

Let the actual distance be $g$. The map - distance from museum to sculpture garden is $d_{m}=1.1$ in. Using the proportion $\frac{1.1}{g}=\frac{1}{3}$. Cross - multiply: $g = 1.1\times3 = 3.3$ km.

Answer:

The actual distance from the hotel to the museum is 2.7 km and the actual distance from the museum to the sculpture garden is 3.3 km.