Krishna travels from point A to point B in 6 hours and returns back to point A from point B in 5 hours. Point A and point B are 220 miles apart along a straight highway. What is the average speed of Krishna for the whole journey?
40 miles/hr
Calculating Average Speed for a Round Trip Journey
The question asks us to find the average speed of Krishna for the entire journey from point A to point B and back to point A. Average speed is defined as the total distance traveled divided by the total time taken for the journey.
Understanding Average Speed
Average speed is different from instantaneous speed or the average speed for individual parts of the journey. It considers the entire path and the entire duration.
The formula for average speed is:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Step-by-Step Calculation
1. Determine the Total Distance Traveled
Krishna travels from point A to point B and then returns from point B to point A. The distance between point A and point B is given as 220 miles.
- Distance from A to B = 220 miles
- Distance from B to A = 220 miles
The total distance is the sum of the distance traveled in both directions.
\(\text{Total Distance} = \text{Distance (A to B)} + \text{Distance (B to A)}\)
\(\text{Total Distance} = 220 \text{ miles} + 220 \text{ miles} = 440 \text{ miles}\)
2. Determine the Total Time Taken
Krishna takes 6 hours to travel from A to B and 5 hours to return from B to A.
- Time taken from A to B = 6 hours
- Time taken from B to A = 5 hours
The total time is the sum of the time taken for each leg of the journey.
\(\text{Total Time} = \text{Time (A to B)} + \text{Time (B to A)}\)
\(\text{Total Time} = 6 \text{ hours} + 5 \text{ hours} = 11 \text{ hours}\)
3. Calculate the Average Speed
Now we use the formula for average speed with the total distance and total time calculated above.
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
\(\text{Average Speed} = \frac{440 \text{ miles}}{11 \text{ hours}}\)
\(\text{Average Speed} = 40 \text{ miles/hr}\)
The average speed of Krishna for the whole journey is 40 miles/hr.
| Leg of Journey | Distance (miles) | Time (hours) | Speed (miles/hr) |
|---|---|---|---|
| A to B | 220 | 6 | \(\frac{220}{6} \approx 36.67\) |
| B to A | 220 | 5 | \(\frac{220}{5} = 44\) |
| Total Journey | 440 | 11 | 40 |
Conclusion
By calculating the total distance traveled (440 miles) and the total time taken (11 hours), we found the average speed for the entire round trip journey to be 40 miles per hour.
Revision Table: Average Speed Calculation
| Concept | Definition/Formula | Application in this problem |
|---|---|---|
| Average Speed | Total Distance / Total Time | \(\frac{440 \text{ miles}}{11 \text{ hours}}\) |
| Total Distance | Sum of distances for each part of the journey | 220 miles (A to B) + 220 miles (B to A) = 440 miles |
| Total Time | Sum of times for each part of the journey | 6 hours (A to B) + 5 hours (B to A) = 11 hours |
Additional Information: Speed vs. Velocity
It's important to distinguish between speed and velocity.
- Speed is a scalar quantity that measures how fast an object is moving, calculated as distance traveled over time. Average speed looks at the total distance over total time.
- Velocity is a vector quantity that measures the rate of change of displacement. It includes both speed and direction. Average velocity is calculated as total displacement over total time.
In this specific journey, Krishna starts at point A and ends at point A. Therefore, the total displacement is 0 miles. The average velocity for the whole journey would be:
\(\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0 \text{ miles}}{11 \text{ hours}} = 0 \text{ miles/hr}\)
This shows that even though the object was moving for a significant amount of time, its average velocity over a round trip where it returns to the starting point is zero.
The question specifically asks for average speed, which depends on the total distance traveled, not displacement.
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:
