A train A is 180 m long,while another train B is 240 m long.A has a speed of 30km/h and B's speed is 40 km/h. If the trains move in opposite directions, find when will ApassBcompletely?

Options

A. a. 21s
B. b. 21.6s
C. c. 26.1s
D. d. 26s

Answer

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

### Step 1: Determine the lengths of the trains
- Train A is 180 meters long.
- Train B is 240 meters long.

### Step 2: Calculate the total length of the trains
- Total length = Length of Train A + Length of Train B
- Total length = 180 m + 240 m = 420 m

### Step 3: Convert the speeds of the trains from km/h to m/s
- Speed of Train A = 30 km/h
- Speed of Train B = 40 km/h

To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
- Speed of Train A in m/s = \( 30 \times \frac{5}{18} = \frac{150}{18} = 8.33 \) m/s
- Speed of Train B in m/s = \( 40 \times \frac{5}{18} = \frac{200}{18} = 11.11 \) m/s

### Step 4: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, we add their speeds:
- Relative speed = Speed of Train A + Speed of Train B
- Relative speed = 8.33 m/s + 11.11 m/s = 19.44 m/s

### Step 5: Calculate the time taken to pass each other completely
Using the formula:
\[ \text{Time} = \frac{\text{Total Length}}{\text{Relative Speed}} \]
- Time = \( \frac{420 \text{ m}}{19.44 \text{ m/s}} \)

Calculating the time:
- Time ≈ 21.6 seconds

### Final Answer
The trains will pass each other completely in approximately **21.6 seconds**.

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