A car covers 4 successive stretches of 3 km each at speed of 10 kmph, 20 kmph, 30 kmph and 60 kmph respectively. The average speed of the car for the entire journey is:
Understanding Average Speed Calculation
The question asks for the average speed of a car over a journey consisting of four equal distances covered at different speeds. Average speed is not simply the average of the individual speeds. Instead, it's calculated by dividing the total distance traveled by the total time taken.
Breaking Down the Journey
The journey is divided into four equal stretches, each 3 km long. The speeds for these stretches are different:
- Stretch 1: Distance = 3 km, Speed = 10 kmph
- Stretch 2: Distance = 3 km, Speed = 20 kmph
- Stretch 3: Distance = 3 km, Speed = 30 kmph
- Stretch 4: Distance = 3 km, Speed = 60 kmph
Calculating Total Distance
The total distance is the sum of the distances of all stretches.
Total Distance = Distance$_1$ + Distance$_2$ + Distance$_3$ + Distance$_4$
Total Distance = 3 km + 3 km + 3 km + 3 km
Total Distance = 4 $\times$ 3 km = 12 km
Calculating Total Time Taken
To find the average speed, we first need to calculate the time taken for each stretch using the formula:
Time = $\frac{\text{Distance}}{\text{Speed}}$
Let's calculate the time for each stretch:
- Time$_1$ ($\(t_1\)$) = $\frac{3 \text{ km}}{10 \text{ kmph}}$ = 0.3 hours
- Time$_2$ ($\(t_2\)$) = $\frac{3 \text{ km}}{20 \text{ kmph}}$ = 0.15 hours
- Time$_3$ ($\(t_3\)$) = $\frac{3 \text{ km}}{30 \text{ kmph}}$ = 0.1 hours
- Time$_4$ ($\(t_4\)$) = $\frac{3 \text{ km}}{60 \text{ kmph}}$ = 0.05 hours
Now, we sum these times to find the total time:
Total Time = \(t_1\) + \(t_2\) + \(t_3\) + \(t_4\)
Total Time = 0.3 + 0.15 + 0.1 + 0.05 hours
Total Time = 0.6 hours
Calculating the Average Speed
Finally, we use the formula for average speed:
Average Speed = $\frac{\text{Total Distance}}{\text{Total Time}}$
Plugging in our calculated values:
Average Speed = $\frac{12 \text{ km}}{0.6 \text{ hours}}$
Average Speed = 20 kmph
Journey Summary Table
| Stretch | Distance (km) | Speed (kmph) | Time (hours) |
|---|---|---|---|
| 1 | 3 | 10 | 0.3 |
| 2 | 3 | 20 | 0.15 |
| 3 | 3 | 30 | 0.1 |
| 4 | 3 | 60 | 0.05 |
| Total | 12 | -- | 0.6 |
Conclusion
The calculations show that the total distance covered is 12 km, and the total time taken is 0.6 hours. Therefore, the average speed for the entire journey is 20 kmph.
Important Questions from Speed Time & Distance (Notes)
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In this context, which of the following statements is CORRECT?- A train travels from Karnal to Kurukshetra at a speed of $90$ km/hr and returns at a speed of $92$ km/hr. If it takes $182$ hours for total travel, then find the distance between Karnal to Kurukshetra. (In Km)
- A cyclist travels at 18 km/hr for 2.5 hours. What distance does he cover?
- A car covers a distance from Hayathnagar to LB nagar at the speed of 64 km/hr and covers the distance from LB nagar to Hayathnagar at the speed of 56 km/hr. What is the average speed (rounded off to nearest integer) of the car?
