A person covers first 30 km in 60 minutes and next 40 km in 30 minutes. What is his average speed for the whole journey?
(140/3) km/hr
Understanding Average Speed Calculation
The question asks us to find the average speed of a person for their entire journey, which is divided into two distinct parts. To calculate the average speed for the whole journey, we need to use the fundamental formula for average speed.
The formula for average speed is:
Average Speed = $\frac{\text{Total Distance Covered}}{\text{Total Time Taken}}$
We are given the distance and time for each segment of the journey. Let's break down the information provided:
- First segment: Distance = 30 km, Time = 60 minutes
- Second segment: Distance = 40 km, Time = 30 minutes
Calculating Total Distance for the Journey
The total distance covered during the whole journey is the sum of the distances covered in each segment.
Total Distance = Distance of Segment 1 + Distance of Segment 2
Total Distance = 30 km + 40 km = 70 km
So, the total distance covered is 70 km.
Calculating Total Time for the Journey
The total time taken for the whole journey is the sum of the time taken for each segment. The time is given in minutes, but the options for speed are in km/hr. We should convert the total time into hours to match the units.
Total Time = Time of Segment 1 + Time of Segment 2
Total Time = 60 minutes + 30 minutes = 90 minutes
Now, let's convert the total time from minutes to hours. There are 60 minutes in 1 hour.
Total Time in hours = $\frac{\text{Total Time in minutes}}{60}$
Total Time in hours = $\frac{90 \text{ minutes}}{60 \text{ minutes/hour}} = \frac{90}{60} \text{ hours} = \frac{3}{2} \text{ hours}$
The total time taken for the journey is $\frac{3}{2}$ hours.
Determining Average Speed
Now that we have the total distance and the total time in appropriate units (km and hours), we can calculate the average speed using the formula:
Average Speed = $\frac{\text{Total Distance}}{\text{Total Time}}$
Average Speed = $\frac{70 \text{ km}}{\frac{3}{2} \text{ hours}}$
To divide by a fraction, we multiply by its reciprocal:
Average Speed = $70 \times \frac{2}{3} \text{ km/hr}$
Average Speed = $\frac{140}{3} \text{ km/hr}$
Comparing with Options
The calculated average speed is $\frac{140}{3}$ km/hr. Let's compare this with the given options:
- $\frac{140}{3}$ km/hr
- 30 km/hr
- $\frac{160}{3}$ km/hr
- 60 km/hr
Our calculated value matches the first option.
Final Answer Conclusion
Based on the calculations of total distance and total time, the average speed for the whole journey is $\frac{140}{3}$ km/hr.
Revision Table: Key Calculations
| Quantity | Value | Units | Calculation/Information |
|---|---|---|---|
| Distance 1 | 30 | km | Given |
| Time 1 | 60 | minutes | Given |
| Distance 2 | 40 | km | Given |
| Time 2 | 30 | minutes | Given |
| Total Distance | 70 | km | 30 km + 40 km |
| Total Time | 90 | minutes | 60 minutes + 30 minutes |
| Total Time | $\frac{3}{2}$ | hours | $\frac{90}{60}$ hours |
| Average Speed | $\frac{140}{3}$ | km/hr | $\frac{\text{Total Distance}}{\text{Total Time}} = \frac{70}{3/2}$ km/hr |
Additional Information: Average Speed vs. Average Velocity
It's important to understand the difference between average speed and average velocity.
- Average Speed: This is the total distance traveled divided by the total time taken. It is a scalar quantity, meaning it only has magnitude. In our problem, we calculated average speed.
- Average Velocity: This is the total displacement divided by the total time taken. It is a vector quantity, meaning it has both magnitude and direction. Displacement is the change in position from the starting point to the ending point, which might be less than the total distance traveled if the path is not a straight line or if the object returns to its starting point.
In this problem, since the journey description only involves distances covered along the path, we are correctly calculating the average speed. If the question involved displacement or direction, we would need to consider average velocity.
Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
