Average Speed Calculation for Round Trip
The problem requires calculating the average speed for a journey covering the same distance twice, but at different speeds.
Key Concepts
- Average Speed Formula: When the distance is the same for two parts of a journey, the average speed is the harmonic mean of the two speeds.
- Formula: Average Speed = \(\frac{2}{\frac{1}{v_1} + \frac{1}{v_2}}\), where \(v_1\) and \(v_2\) are the speeds for the two parts.
Given Information
- Speed from A to B (\(v_1\)) = 13 km/h
- Speed from B to A (\(v_2\)) = 10 km/h
Step-by-Step Calculation
- Apply the Average Speed Formula: Substitute the given speeds into the formula.
Average Speed = \(\frac{2}{\frac{1}{13 \, \text{km/h}} + \frac{1}{10 \, \text{km/h}}}\)
- Find a Common Denominator for the Speeds in the Denominator: The common denominator for 13 and 10 is \(13 \times 10 = 130\).
Average Speed = \(\frac{2}{\frac{10}{130} + \frac{13}{130}}\)
Average Speed = \(\frac{2}{\frac{10 + 13}{130}}\)
Average Speed = \(\frac{2}{\frac{23}{130}}\)
- Simplify the Expression: Divide 2 by the fraction \(\frac{23}{130}\).
Average Speed = \(2 \times \frac{130}{23}\)
Average Speed = \(\frac{260}{23}\) km/h
- Convert to Mixed Fraction: Divide 260 by 23.
\(260 \div 23 = 11\) with a remainder of \(7\).
Therefore, the average speed is \(11\frac{7}{23}\) km/h.
Conclusion
The average speed for the whole journey is \(\frac{260}{23}\) km/h, which is equivalent to \(11\frac{7}{23}\) km/h.
Similar Questions
A cyclist covers 120 meters in 16 seconds on a straight road, then immediately covers 180 meters in 24 seconds on a similar road segment. What is the average speed of the cyclist during the entire journey?
A runner completes one lap of a 200 meter circular track in 50 seconds. What is the average speed of the runner?
If a scooter travels at a constant speed of 25 km per hour, how far will it travel in 4 hours?
- Raj takes $2 \frac{1}{3}$ hours to complete a certain distance at a speed of 51 km/hr. What time would Kiran take to complete the same distance at a speed of 68km/hr?
Important Questions from Speed Time and Distance
The average speed of a train is 180% of the average speed of a car. The car covers a distance of 990 km in 15 hours. The time taken (in hours) by the train to cover the distance of 891 km is:
If Rohit can cover a distance of 1188 km in 22 hours, then what is the speed of Rohit?
A train is moving at 72 km/hrs. The distance covers in 15 minutes by the train is:
If Sonu is driving a car at a speed of 20 m/s, then in how much time Sonu will cover a distance of 936 km?
A person crosses a 1600 m long street in 4 min. What is his speed (in km/h)?
