On a map, the distance from the Phoenix to Globe is 11 inches and the distance from Pheonix to Flagstaff is 18 inches. If actual distance from Pheonix to Flagstaff is 144, are the map's distance proportional to the actual real distance?

Answer 1

To determine if the distances on the map are proportional to the actual real distances, we can calculate the scale of each segment based on the given information.

1. Phoenix to Globe:

   • Map distance: 11 inches
   • We don't have the actual distance from Phoenix to Globe, so we cannot calculate the scale for this portion yet.

2. Phoenix to Flagstaff:

   • Map distance: 18 inches
   • Actual distance: 144 miles

Now, let's calculate the scale for the Phoenix to Flagstaff distance:

\[ \text{Scale} = \frac{\text{Actual Distance}}{\text{Map Distance}} = \frac{144 \text{ miles}}{18 \text{ inches}} = 8 \text{ miles per inch} \]

Now, we have the scale for Phoenix to Flagstaff as 8 miles per inch. To determine if the map's distances from Phoenix to Globe is in proportion with this scale, we need to find the actual distance from Phoenix to Globe.

Assuming we have some reasonable value of actual distance, we can calculate its map equivalent using the identified scale. For the map's distances to be proportional, we would expect:

\[ \text{Map distance (Phoenix to Globe)} / \text{Actual distance (Phoenix to Globe)} = \text{Constant scale} \]

Without knowing the actual distance from Phoenix to Globe, we cannot definitively state the proportionality. If you have that distance, please provide it for further analysis.

In conclusion, we can say that the scale of Phoenix to Flagstaff is 8 miles per inch, but we need the distance for Phoenix to Globe to finalize if all distances follow this proportion.

Answer 2

idk

Answer 3

That's alright! If you don't have the actual distance from Phoenix to Globe, we can discuss the general concept of proportional distances on a map.

To check if two distances on a map are proportional to actual distances, we look for a consistent scale between them. In this case, we calculated a scale for Phoenix to Flagstaff, which is 8 miles for each inch on the map.

For another distance (like Phoenix to Globe) to be proportional, you would take the map distance, apply the same scale, and check if the result matches the known actual distance of that route (if you had it).

If you come across the actual distance from Phoenix to Globe later or if there's another aspect of the question you'd like to explore, feel free to ask!

Answer 4

say it as a word problem

Answer 5

Sure! Here’s a word problem based on your scenario:

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Word Problem:

Jordan is studying a map that shows several cities in Arizona. On the map, the distance from Phoenix to Globe measures 11 inches, while the distance from Phoenix to Flagstaff measures 18 inches. Jordan knows that the actual distance from Phoenix to Flagstaff is 144 miles.

Question:

1. What is the scale of the map in miles per inch based on the distance from Phoenix to Flagstaff?

2. If the scale holds true for all distances represented on the map, how many miles apart are Phoenix and Globe in reality?

3. Are the distances on the map proportional to the actual distances?

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You could solve this by first calculating the scale and then checking if the measurements align accordingly for the distance from Phoenix to Globe. Would you like to work through the problem together?

Answer 6

please answer the word problem

Answer 7

Certainly! Let's work through the word problem step by step.

Given Information:

• Distance from Phoenix to Globe on the map: 11 inches
• Distance from Phoenix to Flagstaff on the map: 18 inches
• Actual distance from Phoenix to Flagstaff: 144 miles

Question 1: What is the scale of the map in miles per inch based on the distance from Phoenix to Flagstaff?

To find the scale, we use the formula:

\[ \text{Scale} = \frac{\text{Actual Distance}}{\text{Map Distance}} = \frac{144 \text{ miles}}{18 \text{ inches}} \]

Calculating this gives:

\[ \text{Scale} = \frac{144}{18} = 8 \text{ miles per inch} \]

Question 2: How many miles apart are Phoenix and Globe in reality?

Now that we know the scale is 8 miles per inch, we can find the actual distance between Phoenix and Globe using the map distance.

\[ \text{Actual Distance (Phoenix to Globe)} = \text{Map Distance} \times \text{Scale} \]

\[ \text{Actual Distance (Phoenix to Globe)} = 11 \text{ inches} \times 8 \text{ miles per inch} = 88 \text{ miles} \]

So, the actual distance from Phoenix to Globe is 88 miles.

Question 3: Are the distances on the map proportional to the actual distances?

We can determine if the distances are proportional by checking if the ratio of the map distances reflects the same ratio of actual distances.

1. The ratio of the map distances:

   • From Phoenix to Globe: 11 inches
   • From Phoenix to Flagstaff: 18 inches
   • The ratio is \( \frac{11}{18} \).

2. The actual distances:

   • Actual distance from Phoenix to Globe: 88 miles
   • Actual distance from Phoenix to Flagstaff: 144 miles
   • The ratio is \( \frac{88}{144} = \frac{11}{18} \) (after simplifying).

Since both ratios \( \frac{11}{18} \) are equal, the map distances are proportional to the actual distances.

Final Summary:

1. The scale of the map is 8 miles per inch.
2. The actual distance from Phoenix to Globe is 88 miles.
3. Yes, the distances on the map are proportional to the actual distances.

If you have any more questions or need clarification, feel free to ask!