A 110 m long train takes 3 seconds to pass a pole. How long is the platform if the train passes it in 15 seconds?

Question

Prepp Team · Accepted Answer

Understanding Train Speed and Platform Length Calculation

This problem involves understanding how the distance covered by a train is measured when it passes a point object like a pole versus when it passes an extended object like a platform. We are given the train's length and the time it takes to pass a pole, which allows us to calculate its speed. Then, we use this speed and the time taken to pass a platform to find the platform's length.

Calculating the Train's Speed

When a train passes a pole (which is considered a point object), the distance covered by the train is equal to its own length. We are given the train's length and the time it takes to pass the pole.

Length of the train = 110 m
Time taken to pass the pole = 3 seconds

The formula for speed is:

$$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$

Using this, we can calculate the speed of the train:

$$ \text{Speed of Train} = \frac{\text{Length of Train}}{\text{Time to pass pole}} $$ $$ \text{Speed} = \frac{110 \text{ m}}{3 \text{ s}} $$

So, the speed of the train is $\frac{110}{3}$ meters per second.

Calculating the Platform's Length

When a train passes a platform, the total distance the train's front end covers from reaching the platform's start until the train's rear end leaves the platform's end is the sum of the train's length and the platform's length. We know the train's speed and the time it takes to pass the platform.

Time taken to pass the platform = 15 seconds
Let the length of the platform be $L$ meters.
Total distance covered = Length of train + Length of platform = $(110 + L)$ m

Using the speed formula again:

$$ \text{Speed} = \frac{\text{Total Distance}}{\text{Time to pass platform}} $$

We can substitute the train's speed and the values for passing the platform:

$$ \frac{110}{3} \text{ m/s} = \frac{(110 + L) \text{ m}}{15 \text{ s}} $$

Now, we can solve for $L$ to find the length of the platform. We can multiply both sides by 15:

$$ \frac{110}{3} \times 15 = 110 + L $$ $$ 110 \times 5 = 110 + L $$ $$ 550 = 110 + L $$

Subtract 110 from both sides to find $L$:

$$ L = 550 - 110 $$ $$ L = 440 $$

Therefore, the length of the platform is 440 meters.

Revision Table: Key Concepts

Concept	Distance Covered	Time Taken
Train passing a point object (pole)	Length of the train	Time taken for the train to pass the object
Train passing an extended object (platform)	Length of the train + Length of the object	Time taken for the train to pass the object

Additional Information on Train Problems

Problems involving trains often deal with relative speed and distance. Here are a few common scenarios:

Train passing a stationary object (pole, person): The distance covered is the train's length. Speed is calculated as Length of Train / Time.
Train passing a stationary extended object (platform, bridge): The distance covered is the train's length plus the object's length. Speed is calculated as (Length of Train + Length of Object) / Time.
Train passing a moving object (another train):
- If moving in the same direction, the relative speed is the difference between their speeds ($v_1 - v_2$). The distance covered for one train to pass the other is the sum of their lengths ($L_1 + L_2$). Time = $(L_1 + L_2) / (v_1 - v_2)$.
- If moving in opposite directions, the relative speed is the sum of their speeds ($v_1 + v_2$). The distance covered is the sum of their lengths ($L_1 + L_2$). Time = $(L_1 + L_2) / (v_1 + v_2)$.

Always ensure units are consistent (e.g., meters for distance, seconds for time, m/s for speed) before performing calculations.