A train can travel 100% faster than a car, Both start from point A at the same time and reach point B 150 km away from A at the same time on the way however train lost about 30 minutes while stopping at a station. Find the speed of car?

Options

A. 115 km/hr
B. 120 km/hr
C. 125 km/hr
D. 150 km/hr

Answer

To solve the problem step by step, we will analyze the information given and use the relationships between speed, time, and distance.

### Step 1: Understand the relationship between the speeds of the train and the car.
The problem states that the train can travel 100% faster than the car. This means if the speed of the car is \( v \), then the speed of the train is \( 2v \).

**Hint:** Remember that "100% faster" means the speed is doubled.

### Step 2: Set up the distance and time relationship.
Both the train and the car travel the same distance of 150 km. The time taken by each can be expressed as:
- Time taken by the car = \( \frac{150}{v} \)
- Time taken by the train = \( \frac{150}{2v} \)

**Hint:** Use the formula \( \text{Distance} = \text{Speed} \times \text{Time} \) to express time in terms of speed.

### Step 3: Account for the train's stoppage.
The train lost 30 minutes (which is \( \frac{1}{2} \) hour) due to a stop. Therefore, the effective time taken by the train is:
\[ \text{Time taken by train} + 0.5 = \frac{150}{2v} + 0.5 \]

**Hint:** Convert minutes to hours for consistency in units.

### Step 4: Set the times equal to each other.
Since both the train and the car reach point B at the same time, we can set their times equal:
\[ \frac{150}{v} = \frac{150}{2v} + 0.5 \]

**Hint:** This equation will help us find the speed of the car.

### Step 5: Solve the equation.
1. Multiply through by \( 2v \) to eliminate the denominators:
\[ 2 \cdot 150 = 150 + v \]
2. Simplify:
\[ 300 = 150 + v \]
3. Rearranging gives:
\[ v = 300 - 150 = 150 \text{ km/h} \]

**Hint:** Isolate \( v \) to find the speed of the car.

### Step 6: Conclusion.
The speed of the car is \( 150 \text{ km/h} \).

**Final Answer:** The speed of the car is 150 km/h.