A car is moving at an average speed of `60(2)/(5) km//hr`. How much distance will it cover in `6(1)/(4)` hours?

Answer

To solve the problem step by step, we need to find the distance covered by a car moving at a speed of \(60\frac{2}{5}\) km/hr over a time of \(6\frac{1}{4}\) hours.

### Step 1: Convert the mixed numbers to improper fractions
1. **Convert the speed**:
\[ 60\frac{2}{5} = \frac{60 \times 5 + 2}{5} = \frac{300 + 2}{5} = \frac{302}{5} \text{ km/hr} \]

2. **Convert the time**:
\[ 6\frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4} \text{ hours} \]

### Step 2: Use the formula for distance
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values we found:
\[ \text{Distance} = \frac{302}{5} \times \frac{25}{4} \]

### Step 3: Multiply the fractions
To multiply the fractions, we multiply the numerators and the denominators:
\[ \text{Distance} = \frac{302 \times 25}{5 \times 4} \]

### Step 4: Simplify the expression
1. **Simplify \(5\) and \(25\)**:
\[ \frac{25}{5} = 5 \]
So, we have:
\[ \text{Distance} = \frac{302 \times 5}{4} \]

2. **Calculate \(302 \times 5\)**:
\[ 302 \times 5 = 1510 \]
Thus:
\[ \text{Distance} = \frac{1510}{4} \]

### Step 5: Divide to find the final distance
Now, divide \(1510\) by \(4\):
\[ \text{Distance} = 377.5 \text{ km} \]

### Final Answer:
The distance covered by the car is \(377.5\) km.

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