If A Car Travels 30km In 40 Minutes, How Long Will It Take To Travel 49km At The Same Speed?

In this article, we will delve into a classic problem of calculating travel time based on speed and distance. We will explore the scenario where a car travels 30km in 40 minutes and determine how long it will take to travel 49km at the same speed. This is a fundamental concept in mathematics and physics, often encountered in everyday situations involving travel and transportation. Understanding how to calculate travel time is essential for planning journeys, estimating arrival times, and optimizing travel routes. This problem involves the core relationship between speed, distance, and time, which is a crucial aspect of kinematics, the branch of physics that describes the motion of objects. By solving this problem, we will reinforce our understanding of these fundamental concepts and their practical applications.

Before diving into the solution, it's important to clearly understand the problem. We are given that a car travels a distance of 30 kilometers in a time of 40 minutes. The key assumption here is that the car maintains a constant speed throughout the journey. This simplifies the calculation as we can directly apply the formula that relates speed, distance, and time. Our goal is to find the time it takes for the same car to travel 49 kilometers, assuming it maintains the same constant speed. This requires us to first determine the car's speed and then use that speed to calculate the time for the longer journey. The problem highlights the direct proportionality between distance and time when speed is constant. A longer distance will naturally take a longer time to cover, provided the speed remains the same. This understanding is crucial for solving the problem accurately and efficiently.

To solve this problem, the first step is to determine the car's speed. Speed is defined as the distance traveled per unit of time. In this case, we know the car travels 30 kilometers in 40 minutes. To express the speed in a standard unit, such as kilometers per hour (km/h), we need to convert the time from minutes to hours. There are 60 minutes in an hour, so 40 minutes is equal to 40/60 = 2/3 hours. Now we can calculate the speed by dividing the distance by the time: Speed = Distance / Time Speed = 30 km / (2/3) hours Speed = 30 km * (3/2) hours Speed = 45 km/h. Therefore, the car's speed is 45 kilometers per hour. This value is crucial for the next step, where we will use it to calculate the time it takes to travel 49 kilometers. Understanding how to convert units and apply the speed formula is essential for solving this type of problem accurately.

Now that we know the car's speed is 45 kilometers per hour, we can calculate the time it will take to travel 49 kilometers. We use the same formula, but this time we rearrange it to solve for time: Time = Distance / Speed. Plugging in the values, we get: Time = 49 km / 45 km/h Time ≈ 1.0889 hours. This result is in hours, but it's often more practical to express the time in minutes. To convert hours to minutes, we multiply by 60: Time ≈ 1.0889 hours * 60 minutes/hour Time ≈ 65.33 minutes. Therefore, it will take approximately 65.33 minutes for the car to travel 49 kilometers at the same speed. This calculation demonstrates the inverse relationship between speed and time when distance is constant. A higher speed would result in a shorter travel time, and vice versa. Understanding this relationship is crucial for making informed decisions about travel planning and time management.

In the previous calculation, we found that it would take approximately 65.33 minutes to travel 49 kilometers. While 65.33 minutes is a valid answer, it's often more precise to express the decimal part of the minutes in seconds. To do this, we focus on the decimal part, which is 0.33 minutes. There are 60 seconds in a minute, so we multiply 0.33 by 60 to get the equivalent in seconds: Seconds = 0.33 minutes * 60 seconds/minute Seconds ≈ 19.8 seconds. Rounding this to the nearest whole number, we get approximately 20 seconds. Therefore, the total time to travel 49 kilometers is approximately 65 minutes and 20 seconds. This level of precision is often required in real-world applications, such as scheduling and logistics, where even small differences in time can be significant. Converting decimal minutes to seconds provides a more granular understanding of the time duration and allows for more accurate planning and execution.

Another way to solve this problem is by using proportions. We know that the car travels 30 kilometers in 40 minutes. We can set up a proportion to find the time it takes to travel 49 kilometers. The proportion can be written as: (30 km) / (40 minutes) = (49 km) / (x minutes) Here, 'x' represents the unknown time we want to find. To solve for x, we can cross-multiply: 30 * x = 49 * 40 30x = 1960 Now, divide both sides by 30: x = 1960 / 30 x ≈ 65.33 minutes. This method gives us the same result as before, approximately 65.33 minutes. We can then convert the decimal part to seconds as we did previously. This approach highlights the concept of direct proportionality, where the ratio of distance to time remains constant when the speed is constant. Proportions are a powerful tool for solving problems involving ratios and rates, and they provide an alternative perspective on this type of travel time calculation.

In conclusion, we have successfully calculated the time it takes for a car to travel 49 kilometers, given that it travels 30 kilometers in 40 minutes at the same speed. We found that it will take approximately 65.33 minutes, or 65 minutes and 20 seconds. We used two methods to solve this problem: the first involved calculating the speed and then using it to find the time, and the second involved setting up a proportion. Both methods yielded the same result, demonstrating the consistency of the underlying principles of speed, distance, and time relationships. This problem illustrates the practical application of mathematical concepts in everyday situations, such as travel planning. Understanding how to calculate travel time is essential for making informed decisions about journeys and schedules. By mastering these fundamental concepts, we can confidently tackle similar problems and apply them to various real-world scenarios.

The final answer is approximately 65 minutes and 20 seconds. This is the time it will take for the car to travel 49 kilometers at the same speed it travels 30 kilometers in 40 minutes.