What is the average speed of the car over the entire distance ?
(i) The car covers the whole distance in four equal stretches at speeds of 10 kmph, 20 kmph 30 kmph and 60 kmph respectively.
(ii) The total time taken is 36 minutes.

Answer

To find the average speed of the car over the entire distance, we can follow these steps:

### Step 1: Understand the Problem
We need to calculate the average speed of a car that travels a total distance divided into four equal stretches at different speeds.

### Step 2: Define the Variables
Let’s assume the total distance covered by the car is \( D \). Since the distance is divided into four equal stretches, each stretch will be \( \frac{D}{4} \).

### Step 3: Assign Speeds to Each Stretch
The speeds for the four stretches are given as:
- First stretch: 10 km/h
- Second stretch: 20 km/h
- Third stretch: 30 km/h
- Fourth stretch: 60 km/h

### Step 4: Calculate Time Taken for Each Stretch
To find the time taken for each stretch, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. For the first stretch:
\[ \text{Time}_1 = \frac{\frac{D}{4}}{10} = \frac{D}{40} \]

2. For the second stretch:
\[ \text{Time}_2 = \frac{\frac{D}{4}}{20} = \frac{D}{80} \]

3. For the third stretch:
\[ \text{Time}_3 = \frac{\frac{D}{4}}{30} = \frac{D}{120} \]

4. For the fourth stretch:
\[ \text{Time}_4 = \frac{\frac{D}{4}}{60} = \frac{D}{240} \]

### Step 5: Calculate Total Time Taken
Now, we can find the total time taken by summing up the times for all stretches:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 + \text{Time}_4 \]
\[ \text{Total Time} = \frac{D}{40} + \frac{D}{80} + \frac{D}{120} + \frac{D}{240} \]

To add these fractions, we need a common denominator, which is 240:
\[ \text{Total Time} = \frac{6D}{240} + \frac{3D}{240} + \frac{2D}{240} + \frac{D}{240} = \frac{12D}{240} = \frac{D}{20} \]

### Step 6: Calculate Average Speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we have:
\[ \text{Average Speed} = \frac{D}{\frac{D}{20}} = 20 \text{ km/h} \]

### Conclusion
The average speed of the car over the entire distance is **20 km/h**.

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