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)
A and B have to travel from place P to place Q following the same route in their respective cars. A drives at $60$ kmph while B drives at $80$ kmph. Find the time taken by B to reach place Q if A takes $12$ hrs.
On a straight road, a bus is $60$ km ahead of a car running in the same direction. After $3$ hours, the car is $90$ km ahead of the bus. If the speed of the bus is $45$ km/h, then what is the speed of the car (in km/h)?
A train running at the speed of $90$ kmph crosses a $250$ m long platform in $26$ seconds. What is the length of the train (in m)?
- A car travels a total distance L. It travels half the distance with speed $v_1$ and the other half with speed $v_2$. The average speed of the car is :
- A cyclist travels at 18 km/hr for 2.5 hours. What distance does he cover?
