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A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?
- a)440
- b)480
- c)520
- d)560
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A train that is 280 metres long, travelling at a uniform speed, crosse...
To solve this problem, we need to understand the concept of relative speed and the time it takes for the train to cross both the platform and the man standing on the platform.
Let's break down the problem step by step:
1. Understanding the situation:
- The train is 280 metres long.
- The train crosses a platform in 60 seconds.
- The train passes a man standing on the platform in 20 seconds.
2. Calculating the speed of the train:
- We know that speed is equal to distance divided by time.
- Let's assume the speed of the train is 'v' m/s.
- The distance covered by the train to cross the platform is the sum of the length of the train and the length of the platform.
- So, the distance covered by the train to cross the platform is 280 + length of the platform.
- The time taken to cross the platform is given as 60 seconds.
- Therefore, the speed of the train is (280 + length of the platform) / 60 m/s.
3. Calculating the distance traveled by the train to pass the man:
- The distance traveled by the train to pass the man is equal to the length of the train.
- The time taken to pass the man is given as 20 seconds.
- Therefore, the distance traveled by the train to pass the man is 280 metres.
4. Setting up the equations:
- We can equate the two distances traveled by the train in terms of time.
- (280 + length of the platform) / 60 = 280 / 20
- Solving this equation will give us the length of the platform.
5. Solving the equation:
- Cross multiplying the equation, we get:
(280 + length of the platform) * 20 = 280 * 60
- Expanding and simplifying the equation, we get:
5600 + 20 * length of the platform = 16800
20 * length of the platform = 11200
length of the platform = 560
Therefore, the length of the platform is 560 metres, which corresponds to option 'D'.
Let's break down the problem step by step:
1. Understanding the situation:
- The train is 280 metres long.
- The train crosses a platform in 60 seconds.
- The train passes a man standing on the platform in 20 seconds.
2. Calculating the speed of the train:
- We know that speed is equal to distance divided by time.
- Let's assume the speed of the train is 'v' m/s.
- The distance covered by the train to cross the platform is the sum of the length of the train and the length of the platform.
- So, the distance covered by the train to cross the platform is 280 + length of the platform.
- The time taken to cross the platform is given as 60 seconds.
- Therefore, the speed of the train is (280 + length of the platform) / 60 m/s.
3. Calculating the distance traveled by the train to pass the man:
- The distance traveled by the train to pass the man is equal to the length of the train.
- The time taken to pass the man is given as 20 seconds.
- Therefore, the distance traveled by the train to pass the man is 280 metres.
4. Setting up the equations:
- We can equate the two distances traveled by the train in terms of time.
- (280 + length of the platform) / 60 = 280 / 20
- Solving this equation will give us the length of the platform.
5. Solving the equation:
- Cross multiplying the equation, we get:
(280 + length of the platform) * 20 = 280 * 60
- Expanding and simplifying the equation, we get:
5600 + 20 * length of the platform = 16800
20 * length of the platform = 11200
length of the platform = 560
Therefore, the length of the platform is 560 metres, which corresponds to option 'D'.
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Community Answer
A train that is 280 metres long, travelling at a uniform speed, crosse...
The train with length 280m passes by a man standing on platform in 20s.
The speed of train is V = 280/20 = 14m/s
Let the length of platform be L
(L + 280 )/60 = 14
L + 280 = 60×14
L = 840 - 280
L = 560 metres
The speed of train is V = 280/20 = 14m/s
Let the length of platform be L
(L + 280 )/60 = 14
L + 280 = 60×14
L = 840 - 280
L = 560 metres
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A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?a)440b)480c)520d)560Correct answer is option 'D'. Can you explain this answer?
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