How Many Cars Can Jacob Wash in 5 Hours? A Comprehensive Guide

Mathematical problem-solving is a crucial skill in various industries, including the car washing sector. In this article, we will explore a scenario where an individual named Jacob washes cars, and we will determine how many cars he can wash in a 5-hour period. We will discuss the different ways to approach this problem and ensure accuracy in our calculations.

Understanding the Problem

The problem states that Jacob can wash 3 cars in 45 minutes. Our goal is to determine how many cars he can wash in a 5-hour period. Let's break down the problem step by step and use different methods to arrive at a comprehensive solution.

Method 1: Using Direct Calculation

First, we need to calculate Jacob's washing rate in cars per minute:

Rate 3 cars / 45 minutes 1 car / 15 minutes

Next, we convert 5 hours into minutes:

5 hours 5 * 60 minutes 300 minutes

Now, we calculate how many cars Jacob can wash in 300 minutes:

Number of cars 300 minutes / 15 minutes per car 20 cars

Therefore, Jacob can wash 20 cars in 5 hours without any assumptions.

Method 2: Simplified Calculation

Another approach involves simplifying the problem. We know that Jacob washes 1 car every 15 minutes. We can determine his rate as:

1 car / 15 minutes 4 cars / 1 hour (since 1 hour 60 minutes)

Therefore, in 5 hours, Jacob can wash:

4 cars per hour * 5 hours 20 cars

Again, we reach the conclusion that Jacob can wash 20 cars in 5 hours.

Considering Real-World Breaks

However, in a real-world scenario, Jacob is likely to take breaks. Let's assume he takes a 15-minute break and a 30-minute lunch break over a 5-hour shift. This means he has lost 45 minutes of work time. Therefore, the actual working time is:

Working time 5 hours * 60 minutes - 45 minutes 300 minutes - 45 minutes 255 minutes

Now, we calculate how many cars he can wash in 255 minutes:

Number of cars 255 minutes / 15 minutes per car 17 cars

Therefore, considering the breaks, Jacob can wash 17 cars in 5 hours.

Conclusion

The most accurate answer without any assumptions, based on the provided data, is that Jacob can wash 20 cars in 5 hours. If we consider real-world breaks and partial worktime, Jacob can wash 17 cars in 5 hours.

Understanding the problem and the context is crucial in mathematical problem-solving. Always use the provided data and avoid making assumptions. By understanding these steps, you can apply similar problem-solving methods to other scenarios in your professional and personal life.