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A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.?
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A train travels a distance of 480 km at a uniform speed. If the speed ...
Problem Statement: A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.
Understanding the problem: The problem statement provides us with the distance travelled by the train and the information that if the speed of the train were to be reduced by 8 km/h, it would have taken 3 more hours to cover the same distance. We need to find the speed of the train.
Solution:
Let us assume that the speed of the train is x km/h.
Case 1: Speed of the train is x km/h
Time taken to cover the distance of 480 km at a speed of x km/h = distance/speed = 480/x
Case 2: Speed of the train is (x-8) km/h
Time taken to cover the distance of 480 km at a speed of (x-8) km/h = distance/speed = 480/(x-8)
We are given that the time taken to cover the distance at the reduced speed is 3 or more hours than the time taken to cover the same distance at the original speed. Therefore, we can write the following inequality:
480/x + 3 ≤ 480/(x-8)
Multiplying both sides by x(x-8), we get:
480(x-8) + 3x(x-8) ≤ 480x
Simplifying the above equation, we get:
480x - 3840 + 3x^2 - 24x ≤ 480x
3x^2 - 24x - 3840 ≤ 0
Dividing both sides by 3, we get:
x^2 - 8x - 1280 ≤ 0
Solving the quadratic equation using the quadratic formula, we get:
x = (8 ± √664)/2
x = 14.56 or x = -6.56
Since the speed of the train cannot be negative, we can discard the negative value. Therefore, the speed of the train is approximately 14.56 km/h.
Final Answer: The speed of the train is approximately 14.56 km/h.
Understanding the problem: The problem statement provides us with the distance travelled by the train and the information that if the speed of the train were to be reduced by 8 km/h, it would have taken 3 more hours to cover the same distance. We need to find the speed of the train.
Solution:
Let us assume that the speed of the train is x km/h.
Case 1: Speed of the train is x km/h
Time taken to cover the distance of 480 km at a speed of x km/h = distance/speed = 480/x
Case 2: Speed of the train is (x-8) km/h
Time taken to cover the distance of 480 km at a speed of (x-8) km/h = distance/speed = 480/(x-8)
We are given that the time taken to cover the distance at the reduced speed is 3 or more hours than the time taken to cover the same distance at the original speed. Therefore, we can write the following inequality:
480/x + 3 ≤ 480/(x-8)
Multiplying both sides by x(x-8), we get:
480(x-8) + 3x(x-8) ≤ 480x
Simplifying the above equation, we get:
480x - 3840 + 3x^2 - 24x ≤ 480x
3x^2 - 24x - 3840 ≤ 0
Dividing both sides by 3, we get:
x^2 - 8x - 1280 ≤ 0
Solving the quadratic equation using the quadratic formula, we get:
x = (8 ± √664)/2
x = 14.56 or x = -6.56
Since the speed of the train cannot be negative, we can discard the negative value. Therefore, the speed of the train is approximately 14.56 km/h.
Final Answer: The speed of the train is approximately 14.56 km/h.
Community Answer
A train travels a distance of 480 km at a uniform speed. If the speed ...
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A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.?
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A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.? 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 A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.?.
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.? 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 A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train travels a distance of 480 km at a uniform speed. If the speed had been 8 kilometre per hour less, then it would have been taken 3 or more to cover the same distance. We need to find the speed of the train.?.
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