Distance Calculation and Speed Problems: A Comprehensive Guide

Understanding speed and distance calculations is crucial for a range of real-world applications, from everyday driving to more complex transportation planning. In this guide, we will explore how to calculate the distance traveled and the remaining distance for a specific scenario. We will also discuss the importance of these calculations in different contexts and provide step-by-step solutions to similar problems.

Scenario: Alex's Journey

Alex is traveling from his home to his friend's village, which is 108 kilometers away. He drives for 1 1/4 hours at a speed of 60 kilometers per hour (km/h). Let's calculate how far Alex is from the village after driving this distance.

Step-by-Step Calculation

Given Data: Speed (v) 60 km/h Time (t) 1.25 h (1 hour and 15 minutes) Total distance to be covered 108 km Distance Traveled in 1.25 hours:

The formula for distance is:

Distance Speed × Time

So,

Distance traveled in 1.25 hours 60 km/h × 1.25 h 75 km

Distance Remaining from the Village:

Distance from the village Total distance - Distance traveled

Distance from the village 108 km - 75 km 33 km

Understanding the Calculation

When Alex drives for 1 1/4 hours at a speed of 60 km/h, he covers a distance of 75 km. The remaining distance to the village is 108 km - 75 km 33 km.

Mathematical Verification

To verify the calculation, we can use the formula:

Distance Speed × Time

Let's calculate the time it takes to travel the entire 108 km at 60 km/h:

Time Distance / Speed

Time 108 km / 60 km/h 1.8 hours

We can also use a proportional approach:

1.8 hours : 108 km 1.25 hours : X km

Cross multiplying gives:

1.8X 1.25 × 108

1.8X 135

X 135 / 1.8 75 km

Since Alex has traveled 75 km in 1.25 hours, the remaining distance is:

108 km - 75 km 33 km

Practical Applications

Understanding how to calculate distance and speed is crucial in various fields, including:

Transportation Planning: Ensuring routes are optimized for delivery or travel time.
Engineering and Construction: Calculating distances for infrastructure projects.
Sports and Fitness: Tracking progress and optimizing training routines.

Correctly calculating distances and speeds can enhance efficiency, accuracy, and safety in these areas.

Conclusion

In this article, we have explored the concept of distance calculation and speed problems. We used a specific scenario involving Alex's journey to demonstrate how to solve such problems step-by-step. Understanding these principles is essential for anyone involved in transportation, engineering, or any field requiring precise distance and speed calculations.