Daksh travels 168 km at 21 km/hr, the next 100 km at 20 km/hr and the next 371 km at 53 km/hr. What is his average speed (in km/hr) for the whole journey?
Calculating Average Speed for Daksh's Journey
This problem requires us to find the average speed for a journey that consists of multiple parts. Each part has a specific distance and a constant speed. To calculate the overall average speed, we need to determine the total distance covered and the total time taken for the entire journey.
Understanding the Average Speed Formula
The formula for average speed is defined as the total distance traveled divided by the total time elapsed. It's crucial to remember that this is not just the average of the speeds of each segment, especially when the durations of each segment are different.
$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $
Step-by-Step Calculation Breakdown
Step 1: Determine the Total Distance
First, we find the sum of the distances covered in each segment of the journey.
- Distance of the first part: $168 \text{ km}$
- Distance of the second part: $100 \text{ km}$
- Distance of the third part: $371 \text{ km}$
Total Distance = $168 \text{ km} + 100 \text{ km} + 371 \text{ km}$
Total Distance = $639 \text{ km}$
Step 2: Calculate the Time for Each Segment
Next, we calculate the time taken for each part of the journey using the formula: $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $.
- Time for Segment 1: Traveling $168 \text{ km}$ at $21 \text{ km/hr}$. $ \text{Time}_1 = \frac{168 \text{ km}}{21 \text{ km/hr}} = 8 \text{ hours} $
- Time for Segment 2: Traveling $100 \text{ km}$ at $20 \text{ km/hr}$. $ \text{Time}_2 = \frac{100 \text{ km}}{20 \text{ km/hr}} = 5 \text{ hours} $
- Time for Segment 3: Traveling $371 \text{ km}$ at $53 \text{ km/hr}$. $ \text{Time}_3 = \frac{371 \text{ km}}{53 \text{ km/hr}} = 7 \text{ hours} $
Step 3: Sum the Times to Find Total Time
Now, we add the times calculated for each segment to find the Total Time spent on the entire journey.
Total Time = $ \text{Time}_1 + \text{Time}_2 + \text{Time}_3 $
Total Time = $ 8 \text{ hours} + 5 \text{ hours} + 7 \text{ hours} $
Total Time = $ 20 \text{ hours} $
Step 4: Compute the Average Speed
Finally, we use the Total Distance and Total Time to calculate the average speed for the whole journey.
$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $
$ \text{Average Speed} = \frac{639 \text{ km}}{20 \text{ hours}} $
$ \text{Average Speed} = 31.95 \text{ km/hr} $
Journey Summary Table
| Journey Segment | Distance (km) | Speed (km/hr) | Time Taken (hours) |
|---|---|---|---|
| 1 | 168 | 21 | 8 |
| 2 | 100 | 20 | 5 |
| 3 | 371 | 53 | 7 |
| Total Journey | 639 | - | 20 |
Therefore, Daksh's average speed for the entire journey is $31.95 \text{ km/hr}$.
Important Questions from Average Speed
- Rishi travels 585 km at 65 km/hr, the next 368 km at 92 km/hr and the next 168 km at 56 km/hr. What is his average speed (in km/hr) for the whole journey? (Round off your answer to two decimal places)
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- A woman travels 488 km at 61 km/hr, a second distance of 468 km at 78 km/hr and a third distance of 210 km at 35 km/hr. Find her average speed for the whole journey (in km/hr).
- A man goes to Nagpur from Visakhapatnam at a speed of 24 km/hr and returns to Visakhapatnam at speed of 40 km/hr, through the same route. What is his average speed (in km/hr) of the entire journey?
- A woman travelled at a speed of 20 m/min for 90 min, and at a speed of 70 m/min for 60 min. Her average speed (in m/min) for the entire journey is:
