Question:
A car covers the first half of the distance between two places at 40 km/h and another half at 50 km/h. The average speed of the car is
A car covers the first half of the distance between two places at 40 km/h and another half at 50 km/h. The average speed of the car is
Show Hint
Avoid the common error of using the arithmetic mean (\( \frac{40+50}{2} = 45 \)). The arithmetic mean only represents average speed if the \textbf{times} spent at each speed are equal. For equal distances, the average speed is always closer to the lower speed.
Updated On: Apr 23, 2026
- 45.00 km/h
- 44.44 km/h
- 43.14 km/h
- 42.04 km/h
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
The problem asks for the average speed of a car that travels two equal distances at different constant speeds.
Step 2: Key Formula or Approach:
Average speed is total distance divided by total time.
When two equal distances (\( d \)) are covered at speeds \( v_1 \) and \( v_2 \), the average speed is the harmonic mean of the two speeds:
\[ v_{avg} = \frac{2 v_1 v_2}{v_1 + v_2} \]
Step 3: Detailed Explanation:
Given:
Speed for first half, \( v_1 = 40 \text{ km/h} \)
Speed for second half, \( v_2 = 50 \text{ km/h} \)
Substituting these values into the harmonic mean formula:
\[ v_{avg} = \frac{2 \times 40 \times 50}{40 + 50} \]
\[ v_{avg} = \frac{4000}{90} \]
\[ v_{avg} = \frac{400}{9} \approx 44.444... \text{ km/h} \]
Step 4: Final Answer:
The average speed of the car is 44.44 km/h.
The problem asks for the average speed of a car that travels two equal distances at different constant speeds.
Step 2: Key Formula or Approach:
Average speed is total distance divided by total time.
When two equal distances (\( d \)) are covered at speeds \( v_1 \) and \( v_2 \), the average speed is the harmonic mean of the two speeds:
\[ v_{avg} = \frac{2 v_1 v_2}{v_1 + v_2} \]
Step 3: Detailed Explanation:
Given:
Speed for first half, \( v_1 = 40 \text{ km/h} \)
Speed for second half, \( v_2 = 50 \text{ km/h} \)
Substituting these values into the harmonic mean formula:
\[ v_{avg} = \frac{2 \times 40 \times 50}{40 + 50} \]
\[ v_{avg} = \frac{4000}{90} \]
\[ v_{avg} = \frac{400}{9} \approx 44.444... \text{ km/h} \]
Step 4: Final Answer:
The average speed of the car is 44.44 km/h.
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