How Far Will the Car Travel in 40 Minutes? A Step-by-Step Guide

Understanding the relationship between speed, distance, and time is crucial for various real-life scenarios, from daily commuting to advanced engineering calculations. In this article, we will explore a classic problem: If a car travels 30 kilometers in one hour, how far will it travel in 40 minutes? We will break down the problem using different methods and highlight the importance of mathematical reasoning.

Method 1: Direct Speed Calculation

Let's start with the simplest method: calculating the car's speed in kilometers per minute and then using that to find the distance in 40 minutes.

Step 1: Calculate the Speed in Kilometers per Minute

The car travels 30 kilometers in 60 minutes. To find the speed in kilometers per minute, we divide the distance by the time in minutes.

Speed 30 km / 60 min 0.5 km/min

This means the car travels 0.5 kilometers every minute.

Step 2: Calculate the Distance in 40 Minutes

Now, we multiply the speed (0.5 km/min) by the time (40 minutes) to find the total distance.

Distance 0.5 km/min * 40 min 20 km

Method 2: Proportional Reasoning

We can also solve this problem using proportional reasoning, which is a fundamental concept in mathematics. Here's how it works:

Step 1: Understand the Proportion

In 60 minutes, the car travels 30 kilometers. We need to find out how far it travels in 40 minutes. This can be represented as a proportion:

60 min : 30 km 40 min : x km

Step 2: Solve for x

To solve for x, we can set up the proportion and solve for the unknown distance (x).

x (30 km * 40 min) / 60 min 20 km

Method 3: Converting Time and Using the Distance-Rate-Time Formula

The distance-rate-time (D RT) formula is a powerful tool for solving problems involving speed, distance, and time. Here's how to apply it to our problem:

Step 1: Convert the Time to Hours

First, convert 40 minutes to hours:

40 min 40 / 60 hours 2/3 hours

Step 2: Use the D RT Formula

Now, we know the speed (R 40 km/h) and the time (T 2/3 hours). Substitute these values into the formula:

D 40 km/h * 2/3 hours 80/3 km 26.67 km (or 26 2/3 km)

Conclusion

The car will travel 20 kilometers in 40 minutes. Whether you use direct speed calculation, proportional reasoning, or the distance-rate-time formula, the result is the same. Understanding these methods can help you solve similar problems with confidence.