A train is moving at a speed of `55 (1)/(5)` km/h. The train travels at the same speed for 6 hours 40 minutes. What is the distance covered by the train?

Answer

To find the distance covered by the train, we can follow these steps:

### Step 1: Convert the speed from mixed fraction to improper fraction
The speed of the train is given as \( 55 \frac{1}{5} \) km/h.
To convert this to an improper fraction:
\[ 55 \frac{1}{5} = \frac{55 \times 5 + 1}{5} = \frac{275 + 1}{5} = \frac{276}{5} \text{ km/h} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place this sum over the original denominator.

### Step 2: Convert travel time from hours and minutes to hours
The train travels for 6 hours and 40 minutes.
To convert this to hours:
\[ 6 \text{ hours} + \frac{40 \text{ minutes}}{60} = 6 + \frac{2}{3} = 6 \frac{2}{3} \text{ hours} \]

**Hint:** To convert minutes to hours, divide the number of minutes by 60.

### Step 3: Calculate the distance using the formula
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Now substituting the values:
\[ \text{Distance} = \frac{276}{5} \text{ km/h} \times 6 \frac{2}{3} \text{ hours} \]
First, convert \( 6 \frac{2}{3} \) to an improper fraction:
\[ 6 \frac{2}{3} = \frac{20}{3} \text{ hours} \]
Now, calculate the distance:
\[ \text{Distance} = \frac{276}{5} \times \frac{20}{3} \]
Multiplying the fractions:
\[ \text{Distance} = \frac{276 \times 20}{5 \times 3} = \frac{5520}{15} \]
Now simplify \( \frac{5520}{15} \):
\[ \text{Distance} = 368 \text{ km} \]

### Final Answer:
The distance covered by the train is **368 km**.

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