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The speeds of two trains are in the ratio 3 : 4. They are going in opposite directions along parallel tracks. If each takes 3 seconds to cross a telegraph post, find the time taken by the trains to cross each other completely?
- a)1 seconds
- b)3 seconds
- c)5 seconds
- d)7 seconds
Correct answer is option 'B'. Can you explain this answer?
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The speeds of two trains are in the ratio 3 : 4. They are going in op...
Speed of both trains = 3 : 4
View all questions of this test
x 3 ↓ : ↓ x 3 ⟶ time
Length = 9m : 12m.
= 3 sec.
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The speeds of two trains are in the ratio 3 : 4. They are going in op...
Given:
- The speeds of two trains are in the ratio 3:4.
- They are going in opposite directions along parallel tracks.
- Each train takes 3 seconds to cross a telegraph post.
To find:
The time taken by the trains to cross each other completely.
Solution:
Let's assume the speeds of the two trains are 3x and 4x, where x is a constant.
When two objects are moving in opposite directions, their speeds are added to find the relative speed. In this case, the relative speed of the two trains is (3x + 4x) = 7x.
Time taken to cross each other:
The time taken to cross each other can be calculated using the formula:
Time = Distance / Speed
Since the distance covered by each train is equal to its length, we can assume the length of each train to be L.
The distance covered by the first train in crossing the second train completely = Length of the first train + Length of the second train = L + L = 2L.
The time taken by the first train to cover this distance is 2L / (3x).
Similarly, the time taken by the second train to cross the first train completely is 2L / (4x).
Therefore, the total time taken by the trains to cross each other completely is:
Time = (2L / (3x)) + (2L / (4x))
Simplifying this expression, we get:
Time = (8L + 6L) / (12x)
Time = 14L / (12x)
Time = 7L / (6x)
Given that each train takes 3 seconds to cross a telegraph post:
From the given information, we know that each train takes 3 seconds to cross a telegraph post. Since the length of each train is L, the speed of each train can be calculated as:
Speed = Distance / Time
Speed = L / 3
Ratio of speeds:
The speeds of the two trains are in the ratio 3:4. Therefore, we can write:
Speed of first train / Speed of second train = 3 / 4
Substituting the values of speed, we get:
(L / 3x) / (L / 3) = 3 / 4
3x / 3 = 3 / 4
4x = 3
x = 3/4
Calculating the time taken:
Substituting the value of x in the expression for time taken, we get:
Time = 7L / (6 * (3/4))
Time = 7L / (18/4)
Time = 7L * (4/18)
Time = 28L / 18
Time = (14L/9) seconds
Conclusion:
Therefore, the time taken by the trains to cross each other completely is (14L/9) seconds. Given that each train takes 3 seconds to cross a telegraph post, the time taken by the trains to cross each other completely is 3 seconds. Hence, the correct answer is option 'B': 3 seconds.
- The speeds of two trains are in the ratio 3:4.
- They are going in opposite directions along parallel tracks.
- Each train takes 3 seconds to cross a telegraph post.
To find:
The time taken by the trains to cross each other completely.
Solution:
Let's assume the speeds of the two trains are 3x and 4x, where x is a constant.
When two objects are moving in opposite directions, their speeds are added to find the relative speed. In this case, the relative speed of the two trains is (3x + 4x) = 7x.
Time taken to cross each other:
The time taken to cross each other can be calculated using the formula:
Time = Distance / Speed
Since the distance covered by each train is equal to its length, we can assume the length of each train to be L.
The distance covered by the first train in crossing the second train completely = Length of the first train + Length of the second train = L + L = 2L.
The time taken by the first train to cover this distance is 2L / (3x).
Similarly, the time taken by the second train to cross the first train completely is 2L / (4x).
Therefore, the total time taken by the trains to cross each other completely is:
Time = (2L / (3x)) + (2L / (4x))
Simplifying this expression, we get:
Time = (8L + 6L) / (12x)
Time = 14L / (12x)
Time = 7L / (6x)
Given that each train takes 3 seconds to cross a telegraph post:
From the given information, we know that each train takes 3 seconds to cross a telegraph post. Since the length of each train is L, the speed of each train can be calculated as:
Speed = Distance / Time
Speed = L / 3
Ratio of speeds:
The speeds of the two trains are in the ratio 3:4. Therefore, we can write:
Speed of first train / Speed of second train = 3 / 4
Substituting the values of speed, we get:
(L / 3x) / (L / 3) = 3 / 4
3x / 3 = 3 / 4
4x = 3
x = 3/4
Calculating the time taken:
Substituting the value of x in the expression for time taken, we get:
Time = 7L / (6 * (3/4))
Time = 7L / (18/4)
Time = 7L * (4/18)
Time = 28L / 18
Time = (14L/9) seconds
Conclusion:
Therefore, the time taken by the trains to cross each other completely is (14L/9) seconds. Given that each train takes 3 seconds to cross a telegraph post, the time taken by the trains to cross each other completely is 3 seconds. Hence, the correct answer is option 'B': 3 seconds.
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The speeds of two trains are in the ratio 3 : 4. They are going in opposite directions along parallel tracks. If each takes 3 seconds to cross a telegraph post, find the time taken by the trains to cross each other completely?a)1 secondsb)3 secondsc)5 secondsd)7 secondsCorrect answer is option 'B'. Can you explain this answer?
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