Question

A vehicle travels $4 \, km$ with speed of $3\, km / h$ and another $4 \, km$ with speed of $5\, km / h$, then it's average speed is

• A. $3.75\, km / h$
• B. $4.25\, km / h$
• C. $3.50 \, km / h$
• D. $4.00\, km / h$

Answer 1

The Correct Option is A

To find the average speed of the vehicle, we need to use the formula for average speed when a vehicle travels different distances at different speeds. The formula for the average speed, \(V_{\text{avg}}\), when distances are the same, is given by:

\(V_{\text{avg}} = \frac{2 \cdot V_1 \cdot V_2}{V_1 + V_2}\)

where \(V_1\) and \(V_2\) are the speeds for the different segments.

In this problem:

• The vehicle travels the first 4 km with a speed of \(V_1 = 3 \, \text{km/h}\).
• The vehicle travels another 4 km with a speed of \(V_2 = 5 \, \text{km/h}\).

Substitute these values into the formula:

\(V_{\text{avg}} = \frac{2 \cdot 3 \cdot 5}{3 + 5} = \frac{30}{8} = 3.75 \, \text{km/h}\)

Therefore, the average speed of the vehicle is 3.75 km/h. This matches the given correct answer.

Let's understand why we use this formula: When the distances are the same, the average speed is the harmonic mean of the speeds. The harmonic mean formula is simplified for equal distances using the expression above.

Conclusion: The correct answer is \(3.75 \, \text{km/h}\), confirming that option 3.75 km/h is the correct one.