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

Answer: (C)

190

Answer 2

Let's solve the problem step by step.

Step 1: Find the speed of the faster train.

Given, the faster train crosses a lamp post in 12 seconds, and it is 160 m long. So, the speed of the faster train (Vf) is:

$Vf = \frac{Distance}{Time}$ = $\frac{160m}{12s} = 13.33 \text{ m/s}$.

Step 2: Calculate the speed of the slower train.

The speed of the slower train (Vs) is given to be 6 km/hr less than the faster train.

First, convert the speed of the faster train to km/hr:

$V_f = 13.33 m/s = 13.33 \times \frac{3600}{1000} = 48 \text{ km/hr}$

Now, subtracting 6 km/hr from 48 km/hr:

$V_s = 48 - 6 = 42 \text{ km/hr} = 11.67 \text{ m/s}$

Step 3: Calculate the length of the slower train. When the two trains cross each other in opposite directions, their relative speed is the sum of their speeds:

$V_{relative} = Vf + Vs = 13.33 + 11.67 = 25 \text{ m/s}$

Now, given that they cross each other in 14 seconds, the combined length of both trains is:

$Distance_{combined} = V_{relative} \times Time = 25 \times 14 = 350m$

Subtracting the length of the faster train from this combined length gives the length of the slower train:

$Length_{slower} = 350 - 160 = 190m$

So, the correct answer is option (c): 190.