Question

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6km/hr less than the faster one, its length, in m, is

• A. 184
• B. 180
• C. 190
• D. 192

Answer 1

The Correct Option is C

It takes 12 seconds for the 160-meter-long faster train to pass a lamppost.

Step 1: Calculate the speed of the faster train

The speed of the faster train is given by: \[ \text{Speed of faster train} = \frac{160}{12} = \frac{40}{3} \, \text{m/s} \]

Step 2: Calculate the speed of the slower train

The speed of the slower train is: \[ \text{Speed of slower train} = \frac{40}{3} - \left(6 \times \frac{5}{18}\right) = \frac{35}{3} \, \text{m/s} \]

Step 3: Determine the relative speed when traveling in opposite directions

When the two trains are traveling in opposite directions, the relative speed is the sum of their individual speeds: \[ \text{Relative speed} = \frac{40}{3} + \frac{35}{3} = 25 \, \text{m/s} \]

Step 4: Calculate the length of the slower train

The two trains will cross each other in 14 seconds. The total length of the two trains is the sum of their lengths. Let \( x \) be the length of the slower train. The relative speed formula is: \[ \text{Relative speed} = \frac{\text{Total length of two trains}}{\text{Time taken to cross each other}} \] Substituting the known values: \[ \frac{160 + x}{25} = 14 \] Solving for \( x \): \[ 160 + x = 14 \times 25 = 350 \] \[ x = 350 - 160 = 190 \, \text{meters} \]

Final Answer:

The length of the slower train is \( \boxed{190} \, \text{meters} \).

Answer 2

To find the length of the other train, we need to first calculate the speed of the faster train and then use it to determine the speed of the other train.

1. Calculate the speed of the faster train:

The faster train is 160 meters long and crosses a lamp post in 12 seconds. The speed \( v \) is given by \( \frac{d}{t} \), where \( d \) is distance and \( t \) is time. Thus:

\[ v = \frac{160}{12} = \frac{40}{3} \, \text{m/s} \]

2. Convert the speed to km/hr:

Since \( 1 \, \text{m/s} = 3.6 \, \text{km/hr} \), we can convert the speed to km/hr: \[ v = \frac{40}{3} \times 3.6 = 48 \, \text{km/hr} \]

3. Calculate the speed of the other train:

It is given that the speed of the other train is 6 km/hr less than the faster one. Therefore: \[ \text{Speed of the other train} = 48 - 6 = 42 \, \text{km/hr} \]

4. Convert the speed of the other train to m/s:

To convert the speed from km/hr to m/s: \[ 42 \, \text{km/hr} = \frac{42 \times 1000}{3600} = \frac{35}{3} \, \text{m/s} \]

5. Calculate the combined speed in m/s:

When the trains are moving in opposite directions, their speeds add up. Thus: \[ \text{Combined speed} = \frac{40}{3} + \frac{35}{3} = 25 \, \text{m/s} \]

6. Find the length of the other train:

The time taken to cross each other is 14 seconds. Thus, the equation is: \[ \text{Total distance} = \text{Relative speed} \times \text{Time} \] Let the length of the other train be \( L \). Therefore: \[ 160 + L = 25 \times 14 \] \[ 160 + L = 350 \] \[ L = 350 - 160 = 190 \, \text{m} \]

Final Answer:

The length of the other train is \( \boxed{190} \) meters.