Analyzing a Parking Lot's Car Population: A Mathematical Riddle Explained

Mathematics often finds a way into seemingly simple riddles and questions. One of these is the classic 'parking lot car dilemma,' where we are asked to determine the number of cars remaining in a parking lot after a specific duration. Let's break down the question and explore the potential interpretations and solutions.

The original question states: 'There are 100 cars in a parking lot. Every hour, 10 drivers leave the parking lot, while another 20 drivers park in the same parking lot. How many cars remain in the parking lot after 3 hours?'

To address the accuracy and interpretative challenges in this question, let's begin by clarifying the potential ambiguities:

Clarifying Ambiguities

1. **Driver's Departure Method**: Does the 10 drivers who leave the lot leave in their cars or on foot? It is reasonable to assume that if they have come to park, they likely leave in their cars. However, to avoid confusion, we'll assume they leave in their cars, thus simplifying the problem.

2. **New Arrivals**: The 20 drivers who park in the lot may either be new to the lot or returning. This doesn't significantly impact the calculation, especially given that the question asks for the number of cars remaining in the lot, not the total number of cars present.

The Mathematical Calculation

With the assumption that the 10 drivers who leave are doing so in their cars, we can proceed to calculate the number of cars remaining in the lot after 3 hours:

Every hour, the net change in the number of cars is:

(20 - 10 10) cars increase

Over 3 hours, the total increase would be:

(10 times 3 30) cars

Starting with 100 cars, the total number of cars remaining after 3 hours would be:

(100 30 130) cars

This aligns with the provided information and solution.

Debating Alternative Interpretations

However, different interpretations might lead to different results. Some might argue that the 20 new drivers each have 2 cars, leading to a total of 40 cars being added each hour. If this were the case, the calculation would be:

Over 3 hours, the total number of cars added would be:

(40 times 3 120) cars

Leading to a total of:

(100 120 220) cars

But this interpretation is less likely given the nature of the riddle and the provided initial condition.

Conclusion

In conclusion, the question “There are 100 cars in a parking lot. Every hour, 10 drivers leave the parking lot, while another 20 drivers park in the same parking lot. How many cars remain in the parking lot after 3 hours?” can be accurately answered by focusing on the net change in the number of cars. Given the assumptions made here, the answer is 130 cars. This example underscores the importance of clear problem statements and the impact of slightly ambiguous wording in mathematical riddles.