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 journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
