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
- A man completes a journey in 11 h. He travels first half of the journey at the speed of 25 km/h and the second half at the speed of 30 km/h. Find the total distance of the 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:
- 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)
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A car travels the first 60 km at 45 km/hr and the next 90 km at 60 km/hr. What is the average speed for the entire journey?
(Round off your answer to two decimal places.)
A scooter travels 40 km at 20 km/hr and returns 60 km at the same speed. What is the average speed?
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Important Questions from Average Speed
A person covers a certain distance at the speed of 60 kmph and returns to the starting point at a speed of 40 kmph . Find the average speed (in km/hour) of the person for the whole journey.
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
A car has to cover 125 kms in 5 hours. What will be the average speed of the car if it has covered 90 kms in the first 3 hours?
A scooter from P to Q travels at 40 km/h and from Q to P at 30 km/h. What is the average speed of the scooter?
A car covers a distance of 100 km at a speed of 60 km/h and another 200 km at a speed of 75 km/h, what is the average speed of the car in km/h for the whole journey? (correct to one decimal place)
