A train can travel 40% faster than a car. Both the train and car start from point A at the same time and reach point B, which is 70 kms away from A, at the same time. On the way, however, the train lost about 15 minutes while stopping at stations. The speed of the train in km/h is:

Options

A. 100
B. 80
C. 112
D. 90

Answer

To solve the problem step-by-step, let's denote the speed of the car as \( S \) km/h. According to the problem, the speed of the train is 40% faster than the speed of the car. Therefore, we can express the speed of the train as:

\[ \text{Speed of the train} = S + 0.4S = 1.4S \text{ km/h} \]

Both the train and the car travel a distance of 70 km to reach point B. However, the train loses 15 minutes due to stops at stations. We need to find the speed of the train.

### Step 1: Calculate the time taken by the car
The time taken by the car to travel 70 km is given by the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{70}{S} \text{ hours} \]

### Step 2: Calculate the time taken by the train
The time taken by the train to travel the same distance (70 km) is:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{70}{1.4S} \text{ hours} \]

However, since the train stops for 15 minutes (which is \( \frac{15}{60} = 0.25 \) hours), the effective time taken by the train is:

\[ \text{Effective Time} = \frac{70}{1.4S} + 0.25 \text{ hours} \]

### Step 3: Set the times equal
Since both the train and the car reach point B at the same time, we can set the two time equations equal to each other:

\[ \frac{70}{S} = \frac{70}{1.4S} + 0.25 \]

### Step 4: Solve for \( S \)
To eliminate the fractions, we can multiply through by \( 1.4S \):

\[ 70 \cdot 1.4 = 70 + 0.25 \cdot 1.4S \]

This simplifies to:

\[ 98 = 70 + 0.35S \]

Now, subtract 70 from both sides:

\[ 28 = 0.35S \]

Now, divide both sides by 0.35:

\[ S = \frac{28}{0.35} = 80 \text{ km/h} \]

### Step 5: Find the speed of the train
Now that we have the speed of the car, we can find the speed of the train:

\[ \text{Speed of the train} = 1.4S = 1.4 \times 80 = 112 \text{ km/h} \]

### Final Answer
The speed of the train is **112 km/h**.

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