Calculating Constant Speed: A Comprehensive Guide

Understanding how to calculate the constant speed of a moving object is an essential aspect of practical mathematics and engineering. This article will explain a specific scenario where we need to calculate the constant speed of a car, discussing the relationship between distance, speed, and time. We will consider two different scenarios to refine our calculation of the constant speed.

The Problem

A car travels a distance of 330 km in two different time intervals: first, in 2 hours and 45 minutes, and then in 3 hours and 12 minutes. We need to determine the constant speed of the car in each of these instances.

First Scenario: 2 Hours and 45 Minutes

We start by calculating the distance in the first scenario where the car covers a 330 km distance in 2.75 hours.

Step 1: Convert the time to hours

The time in hours is calculated as follows:

$$2.75 frac{2 45}{60} frac{245}{60} frac{23}{4} text{ hours}$$

Step 2: Calculate the speed

The speed is calculated using the formula: (text{speed} frac{text{distance}}{text{time}})

$$text{speed} frac{330 text{ km}}{2.75 text{ hours}} 120 text{ km/hr} times 2.75 text{ hours}$$

Step 3: Validate the speed

Upon verifying, the calculated speed is: (text{speed} frac{330 text{ km}}{2.75 text{ hours}} 120 text{ km/hr} times 2.75 text{ hours} 330 text{ km} div 2.75 text{ hours} 120 text{ km/hr} times 2.75 text{ hours} 330 text{ km} div 2.75 text{ hours} 120 text{ km/hr} times 2.75 text{ hours} 330 text{ km} div 2.75 text{ hours} 120 text{ km/hr} times 2.75 text{ hours} 103.125 text{ km/hr})

Conclusion: In this scenario, the constant speed of the car is 103.125 km/hr.

Second Scenario: 3 Hours and 12 Minutes

Next, let's determine the speed if the same distance is covered in 3 hours and 12 minutes.

Step 1: Convert the time to hours

The time in hours is calculated as follows:

$$3.2 frac{3 12}{60} frac{312}{60} 3.2 text{ hours}$$

Step 2: Calculate the speed

The speed is calculated using the formula: (text{speed} frac{text{distance}}{text{time}})

$$text{speed} frac{330 text{ km}}{3.2 text{ hours}} 103.125 text{ km/hr}$$

Conclusion: In this scenario, the constant speed of the car is also 103.125 km/hr.

Implications and Conclusion

The calculations show that, regardless of the time taken, the car travels at a constant speed of 103.125 km/hr. This consistency in speed highlights the importance of understanding the relationship between distance, speed, and time in practical applications such as transportation and logistics.

Additional Information:

If the driver stopped for a while, it would be noted that the car reached its destination after a stop. Although the problem initially did not specify any stops, such stops are common in real-world driving scenarios. Therefore, the car's average speed over the entire distance would be different from its constant speed during the actual driving time.