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:
$ V_{avg} = \frac{2 v_1 v_2}{v_1 + v_2} $Step-by-Step Calculation
- Identify the speeds for each part of the journey.
- Speed of car ($v_1$) = 80 km/h
- Speed of scooter ($v_2$) = 50 km/h
- Apply the average speed formula for equal distances: $ V_{avg} = \frac{2 \times 80 \times 50}{80 + 50} $
- Calculate the numerator: $ 2 \times 80 \times 50 = 2 \times 4000 = 8000 $
- Calculate the denominator: $ 80 + 50 = 130 $
- Divide the numerator by the denominator: $ V_{avg} = \frac{8000}{130} = \frac{800}{13} $
- 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.
Similar Questions
- Wasim travels 455 km at 91 km/hr, the next 390 km at 78 km/hr and the next 476 km at 68 km/hr. What is his average speed (in km/hr) for the whole journey? (Round off your answer to two decimal places)
- Heena covers a certain distance by train at 110 km/h and she returned to the starting point covering the same distance, driving a car at 50 km/h. Find her average speed for the whole journey.
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- An aeroplane flies along the sides of an equilateral triangle at the speed of 300 km/h, 200 km/h and 240 km/h, respectively. The average speed of the plane while flying around the triangle is:
- If a motor car travels the first half of a distance at a speed of 30 km/h and the remaining half distance at a speed of 50 km/h, what will be its average speed?
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- A bus covers the first 50 km of its journey in 95 min and covers the remaining 70 km in 85 min. What is the average speed of the bus?
- A man rides his bicycle for 10 km at an average speed of 12 km/h and further travels 12 km at an average speed of 10 km/h. What is his approximate average speed for the entire trip?
- A person starting from his house covers a distance at 15 km/hr and returns to the starting place at a speed of 10 km/hr. His average speed during the whole journey is:
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Important Questions from Average Speed
A car runs first 275 km at an average speed of 50 km/h and the next 315 km at an average speed of 70 km/h. What is the average speed ( in km/h) for the entire journey?
Akhil rides first 12 km at a speed of 16 km/h and further 6 km at a speed of 20 km/h. Find his average speed (in km/h).
Shyam drives his car 30 km at a speed of 45 km/h and, for the next 1 h 20 m, he drives it at a speed of 51 km/h. Find his average speed (in km/h) for the entire journey.
X and Y travel a distance of 90 km each such that the speed of Y is greater than that of X. The sum of their speeds is 100 km/h and the total time taken by both is 3 hours 45 minutes. The ratio of the speed of X to that of Y is:
If a man travels at \(\frac{1}{x}\) km/h on a journey and returns at \(\rm \frac{1}{x^2}\) km/h, then his average speed for the journey is:
