A train, running at a speed of 36 kmph, takes 60 seconds to cross an electric pole. How much time it will take to cross a platform of length 250 meter?
85 second
Understanding the Train Crossing Problem
This question involves a train moving at a constant speed and asks us to calculate the time it takes to cross two different objects: first an electric pole and then a railway platform. The key concepts here are speed, distance, and time, specifically how they relate when a train crosses a point (like a pole) versus a length (like a platform).
When a train crosses an electric pole (or any point object), the distance covered by the train is equal to its own length. When a train crosses a platform, the total distance covered by the train is equal to the sum of its own length and the length of the platform.
Step 1: Convert Train Speed to Meters per Second
The train's speed is given in kilometers per hour (kmph), but the time and platform length are in seconds and meters. We need to convert the speed from kmph to meters per second (m/s) for consistent units. The conversion factor is $\frac{5}{18}$.
Train Speed = $36 \text{ kmph}$
Converting to m/s:
Speed in m/s = $36 \times \frac{5}{18} \text{ m/s}$
Speed in m/s = $2 \times 5 \text{ m/s}$
Speed in m/s = $10 \text{ m/s}$
So, the train's speed is 10 meters per second.
Step 2: Calculate the Train's Length
The train takes 60 seconds to cross an electric pole. When a train crosses a pole, the distance covered is the train's own length. We know that Distance = Speed $\times$ Time.
Time taken to cross pole = 60 seconds
Speed of train = 10 m/s
Train Length = Speed $\times$ Time
Train Length = $10 \text{ m/s} \times 60 \text{ seconds}$
Train Length = $600 \text{ meters}$
The length of the train is 600 meters.
Step 3: Calculate the Total Distance to Cross the Platform
To cross the platform, the train must cover its own length plus the length of the platform.
Train Length = 600 meters
Platform Length = 250 meters
Total Distance = Train Length + Platform Length
Total Distance = $600 \text{ meters} + 250 \text{ meters}$
Total Distance = $850 \text{ meters}$
The total distance the train needs to cover to cross the platform is 850 meters.
Step 4: Calculate the Time Taken to Cross the Platform
Now we use the formula Time = $\frac{\text{Distance}}{\text{Speed}}$ to find the time taken to cross the platform.
Total Distance = 850 meters
Speed of train = 10 m/s
Time taken = $\frac{\text{Total Distance}}{\text{Speed}}$
Time taken = $\frac{850 \text{ meters}}{10 \text{ m/s}}$
Time taken = $85 \text{ seconds}$
The train will take 85 seconds to cross the platform of length 250 meters.
| Quantity | Value |
|---|---|
| Train Speed (kmph) | 36 kmph |
| Train Speed (m/s) | 10 m/s |
| Time to cross pole | 60 seconds |
| Train Length | 600 meters |
| Platform Length | 250 meters |
| Total Distance (Platform) | 850 meters |
| Time to cross platform | 85 seconds |
Based on our calculations, the time taken to cross the platform is 85 seconds.
Revision Table: Key Concepts for Train Problems
| Concept | Explanation | Distance Covered |
|---|---|---|
| Train crossing a point (pole, person standing) | The train covers its own length. | Length of Train |
| Train crossing a length (platform, bridge, tunnel) | The train covers its length plus the object's length. | Length of Train + Length of Object |
| Train crossing another train (moving in same direction) | Relative speed is difference of speeds. Distance is sum of lengths. | Sum of Lengths |
| Train crossing another train (moving in opposite direction) | Relative speed is sum of speeds. Distance is sum of lengths. | Sum of Lengths |
| Speed Conversion | kmph to m/s: Multiply by $\frac{5}{18}$ m/s to kmph: Multiply by $\frac{18}{5}$ |
N/A |
Additional Information on Time and Distance Problems
Problems involving trains are a common type of time and distance question in quantitative aptitude tests. Mastering the basic formulas and understanding how the distance changes when crossing different types of objects is crucial.
- The fundamental relationship is Distance = Speed $\times$ Time. This can be rearranged to find Speed = $\frac{\text{Distance}}{\text{Time}}$ or Time = $\frac{\text{Distance}}{\text{Speed}}$.
- Always ensure that the units for distance and speed are consistent (e.g., meters and meters/second, or kilometers and kilometers/hour) before performing calculations.
- Relative speed is important when dealing with two moving objects, such as two trains or a train and a person walking.
Practicing different variations of these problems will help build confidence and speed in solving them during exams.
Important Questions from Relative Speed
In a circular race of 2500 m, a man and a woman start from a point towards opposite directions with speeds of 37 km/h and 35 km/h, respectively. After how much time from the start of the race will they meet for the first time?
- X and Yrun a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
A train of length 600 meters passes another train of length 1000 meters moving in the opposite direction in 96 seconds. If the speed of both the trains is the same, then what is the speed of each train?
The distance between Delhi and Patna is $480$ km. A train starts from Delhi and travels towards Patna at a speed of $60$ kmph. Another train starts from Patna towards Delhi at a speed of $80$ kmph, but starts $1$ hour after the first train. In how much time, after the first train started, will they meet each other?
Ram traveling at the speed of 3 km/h reaches 15 minutes late. Had he walked at 4 km/h, he would have reached 15 minutes earlier. How much distance does Ram have to cover?
