Average Speed Calculation for Car and Scooter Journey

The average speed is defined as the total distance traveled divided by the total time taken.

For a journey where an object travels the same distance at two different speeds, $v_1$ and $v_2$, the average speed ($V_{avg}$) can be calculated using the harmonic mean formula:

Step-by-Step Calculation

1. Identify the speeds for each part of the journey.
   • Speed of car ($v_1$) = 80 km/h
   • Speed of scooter ($v_2$) = 50 km/h
2. Apply the average speed formula for equal distances: $ V_{avg} = \frac{2 \times 80 \times 50}{80 + 50} $
3. Calculate the numerator: $ 2 \times 80 \times 50 = 2 \times 4000 = 8000 $
4. Calculate the denominator: $ 80 + 50 = 130 $
5. Divide the numerator by the denominator: $ V_{avg} = \frac{8000}{130} = \frac{800}{13} $
6. Convert the fraction to a decimal and round to two decimal places: $ V_{avg} \approx 61.53846... \text{ km/h} $ Rounded value: $ V_{avg} = 61.54 \text{ km/h} $

Final Answer

The average speed for the whole journey is approximately 61.54 km/h.