Question

A train travels at a speed of 80 km/h for the first 2 hours and then at a speed of 100 km/h for the next 3 hours. What is the average speed of the train for the entire journey?

• A. 88 km/h
• B. 90 km/h
• C. 92 km/h
• D. 94 km/h
• E. 96 km/h

Hint:

A common mistake is to simply average the speeds (e.g., \((80 + 100) / 2 = 90\)). This is incorrect because the train traveled for different amounts of time at each speed. The average speed is a *weighted* average, weighted by the duration of travel at each speed. Always use the formula Total Distance / Total Time.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The average speed is not the simple average of the speeds. It is defined as the total distance traveled divided by the total time taken for the journey.
Step 2: Key Formula or Approach:
The formula for average speed is:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
We also use the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\).
Step 3: Detailed Explanation:
The journey has two parts. We need to calculate the total distance and total time.
Calculate Total Distance:
Distance of the first part:
\[ \text{Distance}_1 = \text{Speed}_1 \times \text{Time}_1 = 80 \, \text{km/h} \times 2 \, \text{h} = 160 \, \text{km} \]
Distance of the second part:
\[ \text{Distance}_2 = \text{Speed}_2 \times \text{Time}_2 = 100 \, \text{km/h} \times 3 \, \text{h} = 300 \, \text{km} \]
Total Distance = Distance\(_1\) + Distance\(_2\):
\[ \text{Total Distance} = 160 \, \text{km} + 300 \, \text{km} = 460 \, \text{km} \]
Calculate Total Time:
Total Time = Time\(_1\) + Time\(_2\):
\[ \text{Total Time} = 2 \, \text{h} + 3 \, \text{h} = 5 \, \text{h} \]
Calculate Average Speed:
Now, we apply the average speed formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{460 \, \text{km}}{5 \, \text{h}} \]
\[ \text{Average Speed} = 92 \, \text{km/h} \]
Step 4: Final Answer:
The average speed of the train for the entire journey is 92 km/h, which corresponds to option (C).