Question

monica attends an environmental fair. there are exhibits in three separate classrooms: the reduce room, the reuse room, and the recycle room. she uses a map to determine how to get to each room.
on the map:

• the distance between the reduce room and the reuse room is 6 inches.
• the distance between the reuse room and the recycle room is 9.1 inches.
• on the map scale, 1 in. represents 15 ft.

enter the scale.
map: 1 in., fair: 15 ft
enter the actual distance, f, from the reduce room to the reuse room.
enter the actual distance, s, from the reuse room to the recycle room.
i want to do this optional task to determine the actual distance, f.
write a proportion using the variable f. then solve for f using means and extremes.
i want to do this optional task to determine the actual distance, s.
write a proportion using the variable s. then solve for s using means and extremes.

Explanation:

Step1: Set up the proportion

The map - scale is 1 in. : 15 ft. Let the map - distance be $d_{m}$ (in inches) and the actual distance be $d_{a}$ (in feet). The proportion is $\frac{d_{m}}{d_{a}}=\frac{1}{15}$.

Step2: Find actual distance from Reduce to Reuse

The map - distance from Reduce to Reuse, $d_{m1}=6$ inches. Substitute into the proportion $\frac{6}{d_{a1}}=\frac{1}{15}$. Cross - multiply: $d_{a1}=6\times15 = 90$ feet.

Step3: Find actual distance from Reuse to Recycle

The map - distance from Reuse to Recycle, $d_{m2}=9.1$ inches. Substitute into the proportion $\frac{9.1}{d_{a2}}=\frac{1}{15}$. Cross - multiply: $d_{a2}=9.1\times15=136.5$ feet.

Answer:

The actual distance from Reduce to Reuse is 90 feet.
The actual distance from Reuse to Recycle is 136.5 feet.