A train of length 100 m takes 1/6 minute to pass over another train 150 m long coming from the opposite direction if the speed of first train is 60 km/h the speed of the second train is:

Options

A. 45 km/h
B. 28 km/h
C. 30 km/h
D. none of these

Answer

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

### Step 1: Understand the problem
We have two trains:
- Train A (length = 100 m, speed = 60 km/h)
- Train B (length = 150 m, speed = x km/h)

Train A takes 1/6 minutes to completely pass Train B.

### Step 2: Convert time from minutes to seconds
Since the time given is in minutes, we need to convert it into seconds for easier calculations.
\[ \text{Time} = \frac{1}{6} \text{ minutes} = \frac{1}{6} \times 60 \text{ seconds} = 10 \text{ seconds} \]

### Step 3: Calculate the total distance covered while passing
When two trains pass each other, the total distance covered is the sum of their lengths:
\[ \text{Total Distance} = \text{Length of Train A} + \text{Length of Train B} = 100 \text{ m} + 150 \text{ m} = 250 \text{ m} \]

### Step 4: Determine the relative speed of the trains
Since the trains are moving towards each other, their relative speed is the sum of their speeds:
\[ \text{Relative Speed} = \text{Speed of Train A} + \text{Speed of Train B} = 60 \text{ km/h} + x \text{ km/h} \]

### Step 5: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Relative Speed in m/s} = \left(60 + x\right) \times \frac{5}{18} \text{ m/s} \]

### Step 6: Use the formula for distance
Using the formula for distance (Distance = Speed × Time), we can set up the equation:
\[ 250 = \left(60 + x\right) \times \frac{5}{18} \times 10 \]

### Step 7: Simplify the equation
First, simplify the right side:
\[ 250 = \left(60 + x\right) \times \frac{50}{18} \]
Now, multiply both sides by 18 to eliminate the fraction:
\[ 250 \times 18 = (60 + x) \times 50 \]
\[ 4500 = (60 + x) \times 50 \]

### Step 8: Divide both sides by 50
\[ \frac{4500}{50} = 60 + x \]
\[ 90 = 60 + x \]

### Step 9: Solve for x
Subtract 60 from both sides:
\[ x = 90 - 60 \]
\[ x = 30 \text{ km/h} \]

### Final Answer
The speed of the second train is **30 km/h**.