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Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.?
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Train travels at a certain average speed for a distance of 63 k m and ...
Understanding the Problem
To find the original speed of the train, let’s define the variables and work through the details.
Variables:
- Let the original speed be "x" km/hr.
- The speed for the second part of the journey is "x + 6" km/hr.
Distances and Times:
- Distance 1: 63 km
- Distance 2: 72 km
- Total time taken: 3 hours
Setting Up the Equations
1. Time for the first part of the journey:
- Time = Distance / Speed
- Time for 63 km = 63 / x hours
2. Time for the second part of the journey:
- Time for 72 km = 72 / (x + 6) hours
3. Total time equation:
- According to the problem, the total time is 3 hours:
- (63 / x) + (72 / (x + 6)) = 3
Solving the Equation
1. Combine the fractions:
- Multiply through by x(x + 6) to eliminate the denominators:
- 63(x + 6) + 72x = 3x(x + 6)
2. Expand and simplify:
- 63x + 378 + 72x = 3x^2 + 18x
- Combine like terms: 135x + 378 = 3x^2 + 18x
3. Rearrange to form a quadratic equation:
- 3x^2 - 117x - 378 = 0
4. Solve using the quadratic formula or factoring.
After solving, you'll find that the original speed (x) comes out to be 18 km/hr.
Conclusion
Thus, the original speed of the train is 18 km/hr.
To find the original speed of the train, let’s define the variables and work through the details.
Variables:
- Let the original speed be "x" km/hr.
- The speed for the second part of the journey is "x + 6" km/hr.
Distances and Times:
- Distance 1: 63 km
- Distance 2: 72 km
- Total time taken: 3 hours
Setting Up the Equations
1. Time for the first part of the journey:
- Time = Distance / Speed
- Time for 63 km = 63 / x hours
2. Time for the second part of the journey:
- Time for 72 km = 72 / (x + 6) hours
3. Total time equation:
- According to the problem, the total time is 3 hours:
- (63 / x) + (72 / (x + 6)) = 3
Solving the Equation
1. Combine the fractions:
- Multiply through by x(x + 6) to eliminate the denominators:
- 63(x + 6) + 72x = 3x(x + 6)
2. Expand and simplify:
- 63x + 378 + 72x = 3x^2 + 18x
- Combine like terms: 135x + 378 = 3x^2 + 18x
3. Rearrange to form a quadratic equation:
- 3x^2 - 117x - 378 = 0
4. Solve using the quadratic formula or factoring.
After solving, you'll find that the original speed (x) comes out to be 18 km/hr.
Conclusion
Thus, the original speed of the train is 18 km/hr.
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Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.?
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Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.?.
Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Train travels at a certain average speed for a distance of 63 k m and then travels a distance of 72km at an average speed of 6 km/hr more than its original speed it takes 3 hrs to cover the total distance. What is its original speed?.?.
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