Calculating Distance Traveled by a Vehicle

Understanding how to calculate the distance traveled by a vehicle using basic principles of speed and time is essential for various applications, from daily commuting to more complex transportation planning. This article will explore the step-by-step method to solve a specific problem: calculating the distance a car travels in 3.75 hours at a speed of 60 km/h (or 60 miles per hour).

Problem Statement

The problem at hand involves a car moving at a constant speed of 60 km/h. If this car takes 3.75 hours to complete a journey, the question is: How far is the journey?

Using the Distance Calculation Formula

The basic formula for distance (D) is given by:

[ D Speed times Time ]

In this formula, Speed (in kilometers per hour or miles per hour) is multiplied by Time (in hours) to find the Distance (in kilometers or miles) covered.

Algebraic Approach

We can express the given information as follows:

- Speed 60 km/h or 60 miles per hour

- Time 3.75 hours, which can be written as the fraction 7/2 hours (since 3.75 3 0.75 3 3/4 15/4 7/2)

Now, substituting these values into the distance formula, we get:

[ D 60 times frac{7}{2} ] [ D frac{420}{2} ] [ D 210 text{ km} ]

This tells us that the journey is 210 kilometers long.

Step-by-Step Solution

Method 1: Direct Calculation

Using the direct method, we can express the journey time as:

- Time 3.75 hours 3 hours and 45 minutes 3 45/60 3.75 hours

Using the formula Distance Speed × Time, we substitute the values:

[ Distance 60 times 3.75 ] [ Distance 210 text{ km} ]

Method 2: Using Units Conversion

Here, we work with the given time in its fractional form:

- Time 3.75 hours 7/2 hours

Again, using the formula Distance Speed × Time, we get:

[ Distance 60 times frac{7}{2} ] [ Distance frac{420}{2} ] [ Distance 210 text{ km} ]

Alternative Approach: Simplified Equation

Another way to solve the problem is to express the time in a simplified form:

- Time 3.75 hours 3 hours and 45 minutes 7/2

Using the formula for distance again:

[ Distance 60 times frac{7}{2} ] [ Distance frac{420}{2} ] [ Distance 210 text{ km} ]

Conclusion

To summarize, through various algebraic approaches, we have determined that the car traveling at 60 km/h takes 3.75 hours to cover a distance of 210 kilometers. This problem is a practical application of the basic distance formula and can be directly solved by multiplying the given speed by the given time.

Understanding these calculations is crucial for various scenarios, including travel planning, logistics, and transportation analysis. By mastering these fundamental concepts, individuals and organizations can efficiently manage and optimize their travel and transportation needs.

For more detailed information and practice, refer to resources on distance, speed, and time calculations, which are essential for a wide range of practical and academic applications.