Average Speed Calculation for Journey
Problem Analysis
The problem involves calculating the average speed for a journey covering the same distance in two different segments, each with a unique speed. We need to find the overall average speed from place A to B and back to A.
- Speed from A to B (\(v_1\)): \(12\) km/h
- Speed from B to A (\(v_2\)): \(3\) km/h
Solution Steps: Harmonic Mean Method
When the distance is the same for different speeds, the average speed is calculated using the harmonic mean formula. The formula for average speed (\(v_{avg}\)) over two segments of equal distance is:
\( v_{avg} = \frac{2}{\frac{1}{v_1} + \frac{1}{v_2}} \)- Substitute the given speeds into the formula: \( v_{avg} = \frac{2}{\frac{1}{12 \text{ km/h}} + \frac{1}{3 \text{ km/h}}} \)
- Calculate the sum of the reciprocals of the speeds: \( \frac{1}{12} + \frac{1}{3} = \frac{1}{12} + \frac{4}{12} = \frac{1+4}{12} = \frac{5}{12} \)
- Calculate the average speed: \( v_{avg} = \frac{2}{\frac{5}{12} \text{ km/h}} = 2 \times \frac{12}{5} \text{ km/h} = \frac{24}{5} \text{ km/h} \)
- Convert the result to a mixed number: \( \frac{24}{5} \text{ km/h} = 4 \frac{4}{5} \text{ km/h} \)
The average speed for the whole journey is \(4 \frac{4}{5}\) km/h.
Similar Questions
- A train goes from A to B at a speed of 40 km/hr and returns from B to A by the same route at 10 km/hr. The average speed (in km/hr) of the train during the two-way journey is:
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- The distances between the points A, B and C are such that AB = 180 km and BC = 240 km. A traveler goes from A to B at 45 km/h, from B to C at 60 km/h, returns from C to B at 40 km/h, and finally from B to A at 30 km/h. Find the average speed (in km/h) for the entire journey.
- ______ is defined as the total path length travelled by an object divided by the total time interval during which the motion has taken place.
- An object travels the first \(200\text{ m}\) in \(20\text{ s}\) and the next \(200\text{ m}\) in \(30\text{ s}\). The average speed of the object is ______.
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- A person drove at 53 kmph for 2.5 hours, then increased his speed by 28 kmph, and reached the destination in another hour. Find the average speed (in kmph) of the person during the entire journey.
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- A car travels 120 km at 60 km/h, then 200 km at 80 km/h, but during the second segment, it experiences a total stoppage time of 20 minutes due to traffic. After that, it covers the final 150 km at 100 km/h. What is the average speed (in km/h, rounded off to one decimal place) of the car for the entire journey including stoppage times?
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.
A train runs at a speed of 28 kmph for 4 hours and 30 kmph for 5 hours and the remaining 40 kms in one hour. What is the average speed per hour?
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?
