The speed of a train is `220%` of the speed of a car . The car covers a distance of `950` km in `19` hours . How much distance will the train cover in `3(1)/(2)` hours ?

Options

A. `380` km
B. `385` km
C. `375` km
D. `285` km

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the speed of the car.
The car covers a distance of 950 km in 19 hours.

To find the speed of the car, we use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ \text{Speed of car} = \frac{950 \text{ km}}{19 \text{ hours}} = 50 \text{ km/h} \]

### Step 2: Calculate the speed of the train.
The speed of the train is given as 220% of the speed of the car.

To find the speed of the train, we calculate:
\[ \text{Speed of train} = 220\% \times \text{Speed of car} = \frac{220}{100} \times 50 \text{ km/h} \]
Calculating this gives:
\[ \text{Speed of train} = 2.2 \times 50 = 110 \text{ km/h} \]

### Step 3: Calculate the distance covered by the train in 3.5 hours.
We need to find out how much distance the train covers in \(3\frac{1}{2}\) hours, which can be converted to an improper fraction:
\[ 3\frac{1}{2} = \frac{7}{2} \text{ hours} \]

Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values:
\[ \text{Distance} = 110 \text{ km/h} \times \frac{7}{2} \text{ hours} \]
Calculating this gives:
\[ \text{Distance} = 110 \times 3.5 = 385 \text{ km} \]

### Final Answer:
The train will cover **385 kilometers** in \(3\frac{1}{2}\) hours.

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