A car covers 15 km, 20 km, 30 km and 12 km at speeds of 20 km/h, 30 km/h, 40 km/h and 30 km/h, respectively. The average speed of the car for the total journey is :

Options

A. 88 km/h
B. 60 km/h
C. 30 km/h
D. 40 km/h

Answer

To find the average speed of the car for the total journey, we will follow these steps:

### Step 1: Calculate the time taken for each segment of the journey.
The formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. **First segment:**
- Distance = 15 km, Speed = 20 km/h
- Time = \( \frac{15}{20} = \frac{3}{4} \) hours

2. **Second segment:**
- Distance = 20 km, Speed = 30 km/h
- Time = \( \frac{20}{30} = \frac{2}{3} \) hours

3. **Third segment:**
- Distance = 30 km, Speed = 40 km/h
- Time = \( \frac{30}{40} = \frac{3}{4} \) hours

4. **Fourth segment:**
- Distance = 12 km, Speed = 30 km/h
- Time = \( \frac{12}{30} = \frac{2}{5} \) hours

### Step 2: Sum the total time taken for the journey.
Now we will add all the times calculated:
\[ \text{Total Time} = \frac{3}{4} + \frac{2}{3} + \frac{3}{4} + \frac{2}{5} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 4, 3, and 5 is 60.

Converting each fraction:
- \( \frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60} \)
- \( \frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60} \)
- \( \frac{3}{4} = \frac{45}{60} \) (already calculated)
- \( \frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60} \)

Now, summing these:
\[ \text{Total Time} = \frac{45}{60} + \frac{40}{60} + \frac{45}{60} + \frac{24}{60} = \frac{154}{60} = \frac{77}{30} \text{ hours} \]

### Step 3: Calculate the total distance covered.
The total distance is:
\[ \text{Total Distance} = 15 + 20 + 30 + 12 = 77 \text{ km} \]

### Step 4: Calculate the average speed.
The average speed is given by:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{77 \text{ km}}{\frac{77}{30} \text{ hours}} = 77 \times \frac{30}{77} = 30 \text{ km/h} \]

Thus, the average speed of the car for the total journey is **30 km/h**.

---