Mastering Complex Math Problems with GPT-4: Advanced Calculations, Real-World Examples, and AI-Powered Solutions

I just got a look at GPT-4 and I’m no math geek, but these look like legit answers to me. For those that are math geeks, go ahead an tell me I’m stupid. But hey, this GPT-4 looks legit to me.

Question for GPT-4:

A train leaves Chicago going to Los Angeles traveling 65 miles per hour, leaves on July 1st at 7am central time, another train leaves St Louis going to Los Angeles traveling 70 miles per hour, leaves on July 1st at 7am central time, and a third train leaves Dallas going 60 miles per hour, leaves on July 1st at 7am central time, which train will arrive in Los Angeles first, second, and third?

The classic question that everyone has seen variations of on standardized testing. If you haven’t seen this question lately, you are probably older like me, but dig back into that mush of a brain you have and I’m sure you have seen this question at one point in your life; or something very similar.

Answer from GPT-4:

To determine which train arrives in Los Angeles first, we need to know the distances between each city and Los Angeles. I don’t have real-time or up-to-date information, but I can provide an approximate answer based on the average distances between these cities. Here are the approximate distances:

1. Chicago to Los Angeles: 2,000 miles
2. St. Louis to Los Angeles: 1,800 miles
3. Dallas to Los Angeles: 1,437 miles

Now, we can calculate the time each train takes to reach Los Angeles using the formula:

Time = Distance / Speed

1. Chicago to Los Angeles: Time = 2,000 miles / 65 mph ≈ 30.77 hours
2. St. Louis to Los Angeles: Time = 1,800 miles / 70 mph ≈ 25.71 hours
3. Dallas to Los Angeles: Time = 1,437 miles / 60 mph ≈ 23.95 hours

Based on these calculations, the order of arrival in Los Angeles would be:

1. Train from Dallas (arrives first)
2. Train from St. Louis (arrives second)
3. Train from Chicago (arrives third)

If anyone is about to take some standardized testing, maybe this above will help you out. Maybe not. Now I figured that if it could do that quickly, I wanted to see if it could go further and calculate how to get all the trains to arrive at the same time, or approximately the same time.

Next Question for GPT-4

What speed would each train need to be adjusted to in order to arrive approximately at the same time?

To make the trains arrive in Los Angeles at approximately the same time, we can use the travel times calculated in the previous answer to find a common time that all three trains can aim for. We will then adjust their speeds accordingly. Let’s use the longest travel time (30.77 hours from Chicago) as our reference.

The travel times were:

1. Chicago to Los Angeles: 30.77 hours
2. St. Louis to Los Angeles: 25.71 hours
3. Dallas to Los Angeles: 23.95 hours

We’ll keep the Chicago train’s speed unchanged at 65 mph, since it already has the longest travel time. Now, we’ll adjust the speeds of the other two trains to match the 30.77-hour travel time.

We can use the formula:

Speed = Distance / Time

1. St. Louis to Los Angeles: Speed = 1,800 miles / 30.77 hours ≈ 58.46 mph (rounded to 58 mph)
2. Dallas to Los Angeles: Speed = 1,437 miles / 30.77 hours ≈ 46.68 mph (rounded to 47 mph)

So, to have all three trains arrive in Los Angeles at approximately the same time, their speeds should be adjusted to:

1. Chicago train: 65 mph (no change)
2. St. Louis train: 58 mph
3. Dallas train: 47 mph

Well I’m sure most of you that are math junkies are going “That is soo simple!” Again, not a math junkie here. Just a fan of cool math, because honestly, I’m math stupid.

New Question for GPT-4

Let’s get away from trains and ask something that might actually help someone in the “real world”. I was just talking about this with someone earlier this morning, and decided to see what GPT-4 knows about this topic.

You are at a craps table in Las Vegas, and you get the chance to roll the dice, what are the odds that you’ll continue to roll before losing your turn?

GPT-4’s Answer

In the game of craps, a player continues to roll the dice until they “lose their turn” by rolling a 7 (a “seven-out”) after the come-out roll or by rolling the initial point number again, which ends the round.

First, let’s understand the odds of rolling a specific number in craps. There are 6 sides on each die, so there are 6 x 6 = 36 possible combinations. The odds of rolling a specific sum can be calculated by determining the number of combinations that result in that sum and dividing by the total possible combinations.

Now, let’s consider the come-out roll, which is the first roll of the dice in a craps round:

1. If you roll a 7 or 11, you win immediately, and the round is over.
2. If you roll a 2, 3, or 12, you lose immediately, and the round is over.
3. If you roll any other number (4, 5, 6, 8, 9, or 10), that number becomes your “point,” and you continue rolling.

To calculate the odds of continuing to roll before losing your turn, let’s first find the probability of rolling a point number on the come-out roll:

• There are six ways to roll a 7, two ways to roll an 11, one way to roll a 2, two ways to roll a 3, and one way to roll a 12. So, there are a total of 6 + 2 + 1 + 2 + 1 = 12 combinations that result in either winning or losing immediately.
• Since there are 36 possible combinations, the probability of rolling a point number on the come-out roll is (36 – 12) / 36 = 24/36 = 2/3 or approximately 66.67%.

Once you have established a point, you’ll continue to roll until you either roll a 7 (which causes you to lose your turn) or roll your point number again (which ends the round). The probability of rolling a 7 is 6/36 = 1/6 or approximately 16.67%. The probability of rolling the point number again depends on which number was rolled initially, as different numbers have different probabilities.

Ultimately, the odds of continuing to roll before losing your turn are dependent on the come-out roll and the point number rolled. It’s important to note that the probability of rolling a 7 increases as the round continues, and eventually, a 7 will be rolled, causing the player to lose their turn.

Conclusion

In conclusion, I did ask GPT-4 to give me the title of this blog post, which it easily spit out. What I have seen so far is pretty cool. Now I do have a new product coming out on April 1st called – To Be or ChatGPT – if you are an affiliate, please consider signing up to promote it.

GPT-4 I can tell is going to be a lot better, and it’s great living in the time period we are living in. I know there is a lot of bad stuff happening in the world right now, but focus on good stuff and the positive.