Calculating Optimal Speed for Distance and Time Constraints: A Problem-Solving Approach
Understanding how to efficiently allocate resources, such as time and speed, is crucial in both academic and practical contexts. This article demonstrates a step-by-step approach to solving a common problem involving distance, time, and speed. We will delve into the details of a specific scenario where a person must cover a given distance within a set time frame, and we'll provide a comprehensive solution to this problem.
The Problem Scenario
A person needs to cover a total distance of 150 kilometers within 15 hours. He has already been traveling at a speed of 11.8 kilometers per hour (km/hr) for 10 hours. The question is: at what speed does he need to travel to cover the remaining distance in the remaining time?
Understanding the Given Information
Total Distance to be Covered: 150 kilometers (km)
Total Time Available: 15 hours
Speed during the First 10 Hours: 11.8 km/hr
Time Elapsed: 10 hours
Step-by-Step Solution
Step 1: Calculate the distance covered in the first 10 hours.
Using the formula:
Distance Speed times; Time
Distance covered in 10 hours:
Distance 11.8 km/hr times; 10 hrs 118 km
Step 2: Determine the remaining distance to be covered.
Remaining Distance Total Distance - Distance Covered
Remaining Distance 150 km - 118 km 32 km
Step 3: Calculate the remaining time.
Remaining Time Total Time - Time Elapsed
Remaining Time 15 hrs - 10 hrs 5 hrs
Step 4: Calculate the speed required to cover the remaining distance in the remaining time.
Using the formula:
Speed Distance / Time
Required Speed Remaining Distance / Remaining Time
Required Speed 32 km / 5 hrs 6.4 km/hr
Therefore, the person needs to travel at a speed of 6.4 km/hr for the remaining time to complete the journey within the given constraints.
Conclusion
In this problem, we demonstrated how to use basic mathematical principles to solve a real-world scenario involving distance, time, and speed. By carefully dissecting the given information and following a logical sequence of steps, we were able to determine the optimal speed required to complete the journey. Such problem-solving skills are invaluable in various fields, including engineering, transportation, and logistics, where efficiency and accuracy are paramount.
Additional Tips
Always break down the problem into smaller, more manageable parts.
Use the appropriate formulas and units to ensure accuracy.
Double-check your calculations to avoid errors.
Understanding these concepts is crucial for students preparing for exams and for professionals in related fields. By practicing similar problems, one can improve their problem-solving skills and gain a deeper understanding of the underlying principles.