Five gasoline stations are located in a region such that any one station is exactly 1 mile away from at least two other stations. This is shown in the diagram to the right.
Part 2
You are currently at station A but read in the newspaper the prices being charged by the other stations are the​ following:
Part 3
Station
Price
B
2.40
C
2.20
D
2.00
E
2.50
F
1.80

Part 4
You seek to buy 20 gallons of gas. What is the greatest price you will pay per gallon at station A if time and travel costs are​ $2 per​ mile?
The highest price you pay for a gallon of gas is ​$enter your response here. ​(round your answer to the nearest​ penny)
.
.
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Question content area right
Part 1
A
B
C
D
E
F
1 mile

Let's break down the problem step by step.

### Step 1: Understand the Cost Calculation
You are currently at Station A and want to buy 20 gallons of gas. However, the other stations have different prices, and you need to consider the cost of travel as well. The cost to travel to another station is $2 per mile.

### Step 2: Calculate the Total Cost for Each Station
For each station, the total cost per gallon includes both the gas price at that station and the additional travel cost per gallon.

#### Station B:
- Distance: 1 mile
- Gas price: $2.40 per gallon
- Travel cost: $ 2 \text{ miles} \times 2 \text{ dollars per mile} = 4 \text{ dollars} $
- Cost per gallon: $ 2.40 + \frac{4}{20} = 2.40 + 0.20 = 2.60 $ dollars per gallon

#### Station C:
- Distance: 1 mile
- Gas price: $2.20 per gallon
- Travel cost: $ 2 \times 1 = 4 $ dollars
- Cost per gallon: $ 2.20 + 0.20 = 2.40 $ dollars per gallon

#### Station D:
- Distance: 1 mile
- Gas price: $2.00 per gallon
- Travel cost: $ 2 \times 1 = 4 $ dollars
- Cost per gallon: $ 2.00 + 0.20 = 2.20 $ dollars per gallon

#### Station E:
- Distance: 1 mile
- Gas price: $2.50 per gallon
- Travel cost: $ 2 \times 1 = 4 $ dollars
- Cost per gallon: $ 2.50 + 0.20 = 2.70 $ dollars per gallon

#### Station F:
- Distance: 1 mile
- Gas price: $1.80 per gallon
- Travel cost: $ 2 \times 1 = 4 $ dollars
- Cost per gallon: $ 1.80 + 0.20 = 2.00 $ dollars per gallon

### Step 3: Determine the Greatest Price You Will Pay
Now that we have the effective cost per gallon for each station, you will choose the station with the highest price, as asked in the problem.

- Station B: $2.60 per gallon
- Station C: $2.40 per gallon
- Station D: $2.20 per gallon
- Station E: $2.70 per gallon
- Station F: $2.00 per gallon

### Final Answer:
The greatest price you will pay per gallon at Station A, including travel costs, is **$2.70** per gallon.

### Would you like any further details or explanations?

Here are 8 related questions you might find interesting:
1. What would be the minimum price per gallon you could pay, including travel costs?
2. If the travel cost was $3 per mile, how would the highest price per gallon change?
3. How does the distance to each station affect the final price you pay?
4. If you could only travel to stations within 2 miles, what would be the best choice?
5. How much would you pay in total for 20 gallons if you chose Station F?
6. If Station E lowered its price to $2.00 per gallon, what would be the impact on your decision?
7. What if you only needed 10 gallons of gas—how would the calculations change?
8. How does the price sensitivity to travel costs affect your choice?

**Tip:** Always consider both direct costs (like the price of gas) and indirect costs (like travel expenses) when making decisions on purchases.

Explore how to calculate the cost of gas at nearby stations including travel costs. This problem involves distance calculations and cost analysis, with specific prices provided for stations B, C, D, E, and F. Discover the highest price you would pay per gallon at station A with a detailed breakdown.

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