Class 10 Exam > Class 10 Questions > A train travels a distance of 480 km at a uni...
Start Learning for Free
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.?
Most Upvoted Answer
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 ...
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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.?
Question Description
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.?.
Solutions 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.? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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.? defined & explained in the simplest way possible. Besides giving the explanation of
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 detailed solution 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.? has been provided alongside types of 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.? theory, EduRev gives you an
ample number of questions to practice 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.? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup