If the speed of a car is `105""1/5` km/h, find the distance covered by it in `3""3/5` hours.

Answer

To solve the problem of finding the distance covered by a car traveling at a speed of \( 105 \frac{1}{5} \) km/h for \( 3 \frac{3}{5} \) hours, we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions

1. **Convert the speed**:
- The speed is given as \( 105 \frac{1}{5} \) km/h.
- To convert this to an improper fraction:
\[ 105 \frac{1}{5} = 105 + \frac{1}{5} = \frac{105 \times 5 + 1}{5} = \frac{525 + 1}{5} = \frac{526}{5} \text{ km/h} \]

2. **Convert the time**:
- The time is given as \( 3 \frac{3}{5} \) hours.
- To convert this to an improper fraction:
\[ 3 \frac{3}{5} = 3 + \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5} \text{ hours} \]

### Step 2: Use the formula for distance

The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values we found:
\[ \text{Distance} = \left(\frac{526}{5} \text{ km/h}\right) \times \left(\frac{18}{5} \text{ hours}\right) \]

### Step 3: Multiply the fractions

To multiply the fractions:
\[ \text{Distance} = \frac{526 \times 18}{5 \times 5} = \frac{9468}{25} \text{ km} \]

### Step 4: Convert the improper fraction to a mixed number

To convert \( \frac{9468}{25} \) to a mixed number:
1. Divide \( 9468 \) by \( 25 \):
- \( 9468 \div 25 = 378 \) remainder \( 18 \).
2. Thus, we can write:
\[ \frac{9468}{25} = 378 \frac{18}{25} \text{ km} \]

### Final Answer

The distance covered by the car is \( 378 \frac{18}{25} \) km.

---