A car covers four successive 7 km distances at speeds of 10km/hour, 20 km/hour, 30km/hour and 60km/hour respectively. Its average speed over this distance is

Options

A. 30km/hour
B. 20km/hour
C. 60km/hour
D. 40km/hour

Answer

To find the average speed of the car over the total distance, we need to calculate the total distance traveled and the total time taken for the journey.

### Step 1: Calculate Total Distance
The car covers four successive distances of 7 km each.

Total Distance = 4 × 7 km = 28 km

### Step 2: Calculate Time Taken for Each Segment
Next, we need to calculate the time taken for each segment of the journey using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. **For the first 7 km at 10 km/h:**
\[ \text{Time}_1 = \frac{7 \text{ km}}{10 \text{ km/h}} = 0.7 \text{ hours} \]

2. **For the second 7 km at 20 km/h:**
\[ \text{Time}_2 = \frac{7 \text{ km}}{20 \text{ km/h}} = 0.35 \text{ hours} \]

3. **For the third 7 km at 30 km/h:**
\[ \text{Time}_3 = \frac{7 \text{ km}}{30 \text{ km/h}} = \frac{7}{30} \text{ hours} \approx 0.2333 \text{ hours} \]

4. **For the fourth 7 km at 60 km/h:**
\[ \text{Time}_4 = \frac{7 \text{ km}}{60 \text{ km/h}} = \frac{7}{60} \text{ hours} \approx 0.1167 \text{ hours} \]

### Step 3: Calculate Total Time
Now, we sum up all the time taken for each segment:

\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 + \text{Time}_4 \]

Calculating this gives:

\[ \text{Total Time} = 0.7 + 0.35 + 0.2333 + 0.1167 = 1.4 \text{ hours} \]

### Step 4: Calculate Average Speed
Finally, we can find the average speed using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values we found:

\[ \text{Average Speed} = \frac{28 \text{ km}}{1.4 \text{ hours}} = 20 \text{ km/h} \]

### Final Answer
The average speed of the car over the total distance is **20 km/h**.

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