On Sunday, I stopped by a gas station near our house. I looked on Costco app and found that at the closest Costco gas station, about 20 miles away, cost 20c per gallon less. My 2023 Corolla Hybrid has the capacity for about 8 gallons and it gives me around 40 miles per gallon. I could have easily calculated whether it is worth filling up locally or to drive to Costco. Of course, one never drives to Costco just to get gas and I end up buying things I really don’t need. Thats a different story.

So I engaged with Gemini, the rebranded Bard from Google. I want to warn you that this is a long post, but an interesting one 🙂 What follows is a conversation, which is the. power of these tools and not one where you ask something and expect an answer right away. Please follow the back and forths below.

At the outset:

• This is a trivial calculation for which one doesn’t need AI. That’s not the point.
• I wanted to see how Gemini interprets my question and whether it provides answers correctly.
• You will see that it understood my question (stated in a relatively complicated way) remarkably well, but its initial answer was not accurate, but the reasoning was pretty good.
• I had to remind Gemini of the mistake and it apologized and corrected it.
• I then followed up with one more question which is not because the answer was wrong, but it made an assumption different from what I would have thought, but there are circumstances when the Gemini scenario can be applicable. And Gemini apologized again!

Every answer came back within 5 seconds of me asking! Here you go:

My first question:

I have a gas station near our house, call it A. I am also a member of Costco, call it B, about 20 miles away. My car gives 40 miles a gallon. I have to decide whether to drive to costco or buy gas in A. Prices in B are typically 20 cents cheaper and my car needs 8 gallons to fill up and I always fill up. when does it make sense to drive to Costco?

Gemini:

It makes sense to drive to Costco (B) when the price difference per gallon between A and B is greater than the cost of the round trip drive to Costco divided by the number of gallons your car holds.

Here’s the breakdown:

Costs associated with driving to Costco (B):

• Gas cost for the round trip: Distance (20 miles) * 2 (round trip) / Fuel Efficiency (40 miles/gallon) = 1 gallon
• Price difference per gallon saved at Costco: $0.20

Costs associated with buying gas at the nearby station (A):

• No round trip cost
• Price difference per gallon lost: $0.20

To determine the price point where driving to Costco becomes beneficial, we need to find the price difference per gallon that offsets the cost of the round trip drive:

Price difference per gallon needed to break even: Cost of round trip drive / Number of gallons needed to fill up = $1 (round trip cost) / 8 gallons = $0.125 per gallon

Therefore, if the price difference per gallon between A and B is greater than $0.125, it makes sense to drive to Costco and fill up.

Here’s an example:

• If the price at station A is $3.20 per gallon and the price at Costco is $3.00 per gallon, the price difference is $0.20 ($3.20 – $3.00).
• Since the price difference ($0.20) is greater than the break-even point ($0.125), driving to Costco would save you money even after accounting for the round trip.

However, this is just a basic analysis. You should also consider other factors like:

• Your time: How much is your time worth? Factor in the time it takes to drive to and from Costco compared to filling up nearby.
• Traffic conditions: Traffic congestion can significantly increase the travel time and negate the cost savings.
• Membership fee: If you’re not already a Costco member, factor in the annual membership fee when calculating your overall cost savings.

By considering all the factors, you can make an informed decision about whether driving to Costco is worth it for your specific situation.

Me:

Price difference calculation is incorrect. the round trip cost is not $1

Gemini:

You’re absolutely right, I made a mistake in the previous calculation. My apologies for the error.

The round trip cost is not $1, it depends on the gas price at station A and the fuel efficiency of your car. Here’s the correct approach:

1. Calculate the round trip gas cost:

• Distance: 20 miles (one way) * 2 (round trip) = 40 miles
• Gas cost for round trip: Distance (40 miles) / Fuel Efficiency (40 miles/gallon) * Price per gallon at A = (40 miles) / (40 miles/gallon) * $X (price at A) = $X

2. Compare the cost difference with the round trip gas cost:

• Price difference per gallon saved at Costco: $0.20

3. Determine the break-even point:

• Price difference per gallon needed to break even: Round trip gas cost / Number of gallons needed to fill up = $X (round trip gas cost) / 8 gallons

Therefore, it makes sense to drive to Costco when the price difference per gallon between A and B is greater than the calculated break-even point.

Example:

• If the price at station A is $3.20 per gallon:

• Round trip gas cost: (40 miles) / (40 miles/gallon) * $3.20/gallon = $3.20
• Break-even price difference: $3.20 / 8 gallons = $0.40 per gallon

• In this example, you need a price difference greater than $0.40 per gallon at Costco to justify the drive.

I apologize for the previous misunderstanding and hope this corrected explanation is helpful!

Me:

Why is the roundtrip cost based on pumping the gas at A? If I am going to B, which is cheaper, shouldn’t that price be used?

Gemini:

You’re absolutely right, I made another error in the previous explanation. The round trip cost should not be based on the gas price at station A, but rather the actual price of gas you will be using for the trip, regardless of whether you pump at A or B.

Here’s the corrected approach:

1. Calculate the round trip gas cost:

• Distance: 20 miles (one way) * 2 (round trip) = 40 miles
• Gas cost for round trip: Distance (40 miles) / Fuel Efficiency (40 miles/gallon) * Price per gallon you plan to use = (40 miles) / (40 miles/gallon) * $X (price) = $X

2. Use the intended gas price:

• In this case, you are planning to buy gas at Costco (B), so the price to use in the formula is the price at B.

3. Compare the cost difference with the round trip gas cost:

• Price difference per gallon saved at Costco: $0.20

4. Determine the break-even point:

• Price difference per gallon needed to break even: Round trip gas cost / Number of gallons needed to fill up = $X (round trip gas cost using price at B) / 8 gallons

Therefore, it makes sense to drive to Costco when the price difference per gallon between A and B is greater than the calculated break-even point.

Example:

• If the price at station B is $3.00 per gallon:

• Round trip gas cost: (40 miles) / (40 miles/gallon) * $3.00/gallon = $3.00
• Break-even price difference: $3.00 / 8 gallons = $0.375 per gallon

• In this example, you need a price difference greater than $0.375 per gallon between A and B to justify the drive to Costco, considering the gas cost for the round trip.

I apologize for the repeated errors in my previous explanations and appreciate you pointing out my mistakes. I am still under development and learning to improve my accuracy.