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A train 150 metres long crosses a pole in 15 seconds and crosses another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train in km/hr is
- a)52
- b)56
- c)54
- d)58
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A train 150 metres long crosses a pole in 15 seconds and crosses anoth...
A train 150 metres long crosses a pole in 15 seconds
Distance covered to cross the pole = Length of the train = 150 m
Time required = 15 sec
∴ Speed of the first train
= Distance covered/Required time
= 150m/15sec = 10 m/sec
Let, Speed of the second train = ‘x’ m/sec
∵ Trains were travelling in opposite directions
∴ Relative velocity of first train with respect to second train
= (10 + x) km/sec
Given,
First train takes 12 second to cross the second train moving in opposite direction
∴ Distance covered to cross second train
= Length of first train + Length of second train
∵ Length of second train = Length of first train
= 150 m + 150 m = 300 m
And, Time required = 12 sec
∴ Speed of the first train = Distance covered/Required time
⇒ 10 + x = 300/12
⇒ 120 + 12x = 300
⇒ 12x = 180
Distance covered to cross the pole = Length of the train = 150 m
Time required = 15 sec
∴ Speed of the first train
= Distance covered/Required time
= 150m/15sec = 10 m/sec
Let, Speed of the second train = ‘x’ m/sec
∵ Trains were travelling in opposite directions
∴ Relative velocity of first train with respect to second train
= (10 + x) km/sec
Given,
First train takes 12 second to cross the second train moving in opposite direction
∴ Distance covered to cross second train
= Length of first train + Length of second train
∵ Length of second train = Length of first train
= 150 m + 150 m = 300 m
And, Time required = 12 sec
∴ Speed of the first train = Distance covered/Required time
⇒ 10 + x = 300/12
⇒ 120 + 12x = 300
⇒ 12x = 180
Most Upvoted Answer
A train 150 metres long crosses a pole in 15 seconds and crosses anoth...
To solve this problem, we can use the concept of relative speed. Let's break down the information given:
- Length of the train = 150 meters
- Time taken to cross a pole = 15 seconds
- Time taken to cross another train = 12 seconds
We need to find the speed of the second train in km/hr.
Let's assume the speed of the first train is 'x' m/s and the speed of the second train is 'y' m/s.
1. Time taken to cross a pole:
The length of the train is equal to the distance traveled by the train while crossing the pole. So, we can use the formula:
Distance = Speed × Time
150 = x × 15
=> x = 150/15
=> x = 10 m/s
2. Time taken to cross another train:
When two objects are moving towards each other, their relative speed is the sum of their individual speeds. In this case, the relative speed of the two trains is (x + y) m/s. The distance traveled by the train while crossing the other train is equal to the sum of their lengths.
Distance = (Length of the train + Length of the other train) = (150 + 150) = 300 meters
Using the formula:
Distance = Speed × Time
300 = (x + y) × 12
=> 300 = (10 + y) × 12
=> 300 = 120 + 12y
=> 12y = 300 - 120
=> 12y = 180
=> y = 180/12
=> y = 15 m/s
3. Converting the speed to km/hr:
To convert the speed from m/s to km/hr, we multiply the speed by 18/5.
Speed of the second train = y × (18/5) = 15 × (18/5) = 54 km/hr
Therefore, the speed of the second train is 54 km/hr (option C).
- Length of the train = 150 meters
- Time taken to cross a pole = 15 seconds
- Time taken to cross another train = 12 seconds
We need to find the speed of the second train in km/hr.
Let's assume the speed of the first train is 'x' m/s and the speed of the second train is 'y' m/s.
1. Time taken to cross a pole:
The length of the train is equal to the distance traveled by the train while crossing the pole. So, we can use the formula:
Distance = Speed × Time
150 = x × 15
=> x = 150/15
=> x = 10 m/s
2. Time taken to cross another train:
When two objects are moving towards each other, their relative speed is the sum of their individual speeds. In this case, the relative speed of the two trains is (x + y) m/s. The distance traveled by the train while crossing the other train is equal to the sum of their lengths.
Distance = (Length of the train + Length of the other train) = (150 + 150) = 300 meters
Using the formula:
Distance = Speed × Time
300 = (x + y) × 12
=> 300 = (10 + y) × 12
=> 300 = 120 + 12y
=> 12y = 300 - 120
=> 12y = 180
=> y = 180/12
=> y = 15 m/s
3. Converting the speed to km/hr:
To convert the speed from m/s to km/hr, we multiply the speed by 18/5.
Speed of the second train = y × (18/5) = 15 × (18/5) = 54 km/hr
Therefore, the speed of the second train is 54 km/hr (option C).
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A train 150 metres long crosses a pole in 15 seconds and crosses another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train in km/hr isa)52b)56c)54d)58Correct answer is option 'C'. Can you explain this answer?
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