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?
59
Understanding Average Speed Calculation
The question asks us to find the average speed of a car for its entire journey, which is completed in two distinct parts with different speeds.
Average speed is defined as the total distance covered divided by the total time taken for the journey. The formula is:
To solve this problem, we need to calculate the total distance traveled and the total time taken for the entire journey.
Step-by-Step Journey Analysis
The journey is divided into two parts:
- Part 1: Distance = 275 km, Average Speed = 50 km/h
- Part 2: Distance = 315 km, Average Speed = 70 km/h
Calculating Time for Each Part
We can calculate the time taken for each part of the journey using the formula: Time = Distance / Speed.
Time taken for Part 1:
Time taken for Part 2:
Calculating Total Time and Distance
Now, let's find the total distance and total time for the entire journey.
Total Distance:
Total Time:
Calculating Average Speed for the Entire Journey
Using the total distance and total time, we can now calculate the average speed for the entire journey.
The average speed for the entire journey is 59 km/h.
| Segment | Distance (km) | Average Speed (km/h) | Time (hours) |
|---|---|---|---|
| Part 1 | 275 | 50 | 5.5 |
| Part 2 | 315 | 70 | 4.5 |
| Total | 590 | - | 10 |
Therefore, the average speed for the entire journey is 59 km/h.
Revision Table: Key Concepts
| Concept | Formula | Units |
|---|---|---|
| Speed | Distance / Time | e.g., km/h, m/s |
| Distance | Speed × Time | e.g., km, m |
| Time | Distance / Speed | e.g., hours, seconds |
| Average Speed | Total Distance / Total Time | Same as speed units |
Additional Information: Average Speed vs. Average of Speeds
It's important to distinguish between average speed and the simple average (arithmetic mean) of the speeds.
- Average Speed (Correct): Calculated as $\frac{\text{Total Distance}}{\text{Total Time}}$. This is the correct way to find the average speed over a journey with varying speeds or distances.
- Average of Speeds (Incorrect): Calculated as $\frac{\text{Sum of Speeds}}{\text{Number of Speeds}}$. This method is generally incorrect unless the time taken for each segment is equal. In this problem, the times (5.5 hours and 4.5 hours) are not equal, so a simple average of 50 km/h and 70 km/h ($\frac{50+70}{2} = 60$ km/h) would be incorrect.
The correct approach is always to use the total distance and total time.
Important Questions from Average Speed
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:
With an average speed of 45 km/h, a train reaches its destination on time. If it goes with an average speed of 30 km/h, it is late by 15 minutes. The total journey is:
