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 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.
Important Questions from Average Speed
A car covers the first 41 km of its journey in 45 min and covers the remaining 23 km in 35 min. What is the average speed (in m/sec) of the car?
Akhil drives a car from his home to office at an average speed of 50 km/h and reaches office 10 minutes early. But one day due to some problem with the car, he could drive at an average speed of 30 km/h only and reached office 10 minutes late. How far is his office from home ?
During a flight of 900 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 300 km/h and the time of flight increased by 30 min. The original duration of the flight was :
If a man travels from A to B at a speed of 50 km/h and returns by increasing his speed by 40%, then find his average speed (to 2 decimal places) for both the trips.
A man travels a distance of 420 km by train which moves at the speed of 75 km/h and returns back by car at the speed of 50 km/h. Find his average speed for the whole journey.
