Re-explain this solution in more depth — clearer step-by-step reasoning a student can follow, with the 'why' behind each step. Problem: A train travels 240 km in 3 hours. What is its average speed in km/h? Show your work. Current solution: The average speed of the train is 80 km/h. Show your work: The formula for average speed is: Speed = Distance / Time Given: Distance = 240 km Time = 3 hours Substitute the values into the formula: Speed = 240 km / 3 hours Speed = 80 km/h
Physics
ScanSolve AI Answer
Answer
The average speed of the train is 80 km/h.
Step-by-step solution
7 stepsShow your work:
Let's break down the problem and solution step-by-step:
Understand what "average speed" means.
- Why: Before solving, it's crucial to understand the concept. Average speed tells us how much distance an object covers, on average, for each unit of time it travels. It doesn't account for variations in speed during the journey (like speeding up or slowing down), but rather gives an overall rate.
Identify the correct formula for average speed.
- Formula: Average Speed = Total Distance / Total Time
- Why: This formula is derived directly from the definition of speed. If you want to know how fast something is moving on average, you divide the total distance it traveled by the total amount of time it took to travel that distance.
Extract the given information from the problem.
- Given:
- Total Distance traveled by the train = 240 km
- Total Time taken for the journey = 3 hours
- Why: Clearly listing the known values helps organize the problem and ensures you use the correct numbers in your calculation.
- Given:
Check the units.
- Units: The distance is in kilometers (km) and the time is in hours (h). The question asks for the speed in km/h.
- Why: It's important to ensure that the units are consistent with the desired output unit. If, for example, the time was given in minutes, we would first need to convert it to hours to get an answer in km/h. In this case, the units are already compatible, so no conversion is needed.
Substitute the given values into the formula.
- Formula: Average Speed = Total Distance / Total Time
- Substitution: Average Speed = 240 km / 3 hours
- Why: This is where you plug the specific numbers from the problem into the general formula, preparing for the calculation.
Perform the calculation.
- Calculation: 240 ÷ 3 = 80
- Why: This step executes the mathematical operation required by the formula.
State the final answer with the correct units.
- Result: Average Speed = 80 km/h
- Why: The units are crucial for giving meaning to the numerical answer. "80" alone doesn't tell us much, but "80 km/h" clearly indicates the rate at which the train traveled.
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