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Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.?
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Two trains, train A from Kolkata to Patna and train B from Patna to Ko...
Problem Statement: Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.
Solution:
To solve this problem, we can use the formula:
Distance = Speed x Time
Let the speed of train A be x and the speed of train B be y. Let the distance between Kolkata and Patna be d.
When the two trains meet, the total distance covered by both trains is d.
Thus, we can write:
Distance covered by train A + Distance covered by train B = d
Using the formula, we get:
(x+y) x 1 + (y+x) x 4 = d
Simplifying this equation, we get:
5x + 5y = d
Dividing both sides by 5, we get:
x + y = d/5
Now, we can use the formula again to find the distance covered by each train:
Distance covered by train A = x x 1 = x
Distance covered by train B = y x 4 = 4y
Since the total distance covered is d, we can write:
x + 4y = d
Substituting the value of x + y from the earlier equation, we get:
x + 4y = 5(x+y)
Simplifying, we get:
x = 4y
Thus, the speed of train A is twice the speed of train B, as required to be proved.
Solution:
To solve this problem, we can use the formula:
Distance = Speed x Time
Let the speed of train A be x and the speed of train B be y. Let the distance between Kolkata and Patna be d.
When the two trains meet, the total distance covered by both trains is d.
Thus, we can write:
Distance covered by train A + Distance covered by train B = d
Using the formula, we get:
(x+y) x 1 + (y+x) x 4 = d
Simplifying this equation, we get:
5x + 5y = d
Dividing both sides by 5, we get:
x + y = d/5
Now, we can use the formula again to find the distance covered by each train:
Distance covered by train A = x x 1 = x
Distance covered by train B = y x 4 = 4y
Since the total distance covered is d, we can write:
x + 4y = d
Substituting the value of x + y from the earlier equation, we get:
x + 4y = 5(x+y)
Simplifying, we get:
x = 4y
Thus, the speed of train A is twice the speed of train B, as required to be proved.
Community Answer
Two trains, train A from Kolkata to Patna and train B from Patna to Ko...
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Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.?
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Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.?.
Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two trains, train A from Kolkata to Patna and train B from Patna to Kolkata start simultaneously. After they meet, the trains reach their destinations after 1 hour and 4 hours respectively. Prove that the speed of train A is twice that of train B.?.
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