On a map, the distance from the phoenix to globe is 11 inches and the distance from phoenix to flagstaff is 88 miles and the distance from phoenix to flagstaff is 144, are the map's distances proportional to the actual real distance?

Answer 1

To determine if the map's distances are proportional to actual distances, we need to establish a scale for both pairs of distances given:

1. The distance from Phoenix to Globe is 11 inches on the map, and the actual distance is 88 miles.
2. The distance from Phoenix to Flagstaff is 144 miles on the map, and we will consider the stated distance of 88 miles as the correct actual distance.

We can find the scale for each pair of points:

For Phoenix to Globe:

• Map Distance: 11 inches
• Actual Distance: 88 miles

To find the scale: \[ \text{Scale (inches per mile)} = \frac{\text{Map Distance}}{\text{Actual Distance}} = \frac{11 \text{ inches}}{88 \text{ miles}} = \frac{1}{8} \text{ inches per mile} \]

For Phoenix to Flagstaff:

• Map Distance: 144 inches
• Actual Distance: 88 miles

To find the scale: \[ \text{Scale (inches per mile)} = \frac{\text{Map Distance}}{\text{Actual Distance}} = \frac{144 \text{ inches}}{88 \text{ miles}} = \frac{72}{44} = \frac{18}{11} \text{ inches per mile} \]

Now, we need to compare the scale obtained from both distances. For the distances to be proportional, both ratios must be equal when expressed in the same units.

• Scale from Phoenix to Globe: \( \frac{1}{8} \) inches per mile
• Scale from Phoenix to Flagstaff: \( \frac{18}{11} \) inches per mile

Since \( \frac{1}{8} \neq \frac{18}{11} \), the scales are not proportional.

Therefore, the map’s distances from Phoenix to Globe and Phoenix to Flagstaff are not proportional to the actual real distances.