Class 10 Exam > Class 10 Questions > A train travels a distance of 480 km at unif...
Start Learning for Free
A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train.
? Related: Using Quadratic Formula
Most Upvoted Answer
A train travels a distance of 480 km at uniform speed.If the speed ha...
Problem
A train travels a distance of 480 km at uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Solution
Let's assume the original speed of the train as x km/h.
According to the problem:
- Distance travelled by the train = 480 km
- Time taken at speed x = t
- Time taken at speed x - 8 km/h = t + 3
Deriving the equation
Using the formula:
Distance = Speed x Time
We can write:
- 480 = xt
- 480 = (x - 8)(t + 3)
Simplifying the second equation:
- 480 = xt - 8t + 3x - 24
- 504 = xt + 3x - 8t
- 504 = x(t + 3) - 8t
Substituting the value of xt from the first equation:
- 504 = 480 + 3x - 8t
- 24 = 3x - 8t
Now, we have two equations:
- 480 = xt
- 24 = 3x - 8t
Using Quadratic Formula
Let's solve the second equation for t:
- 24 = 3x - 8t
- 8t = 3x - 24
- t = (3x - 24)/8
Substituting this value of t in the first equation:
- 480 = x((3x - 24)/8)
- 3840 = 3x2 - 24x
- 3x2 - 24x - 3840 = 0
Using the quadratic formula:
x = (-b ± √(b2 - 4ac))/2a
We get:
Community Answer
A train travels a distance of 480 km at uniform speed.If the speed ha...
Answer..40km/hr.
Explanation:
Total Distance S=480km
Formula For Speed
speed=distancetime
Hence distance=speed×time
Case-I
let the uniform speed of Train =vkmh
and the time taken to complete distance =(t)hour
Distance S=speed×time=vt -(equation 1)
Case-II
If speed has been 8km/h less then train would have taken 3 hours more to cover the same distance.
Now in this situation
speed of train =(v−8)kmh
and Time taken to complete distance =(t+3)hour
Distance S=speed×time=(v−8)(t+3) - (equation 2)
Since Distance for both cases are same .
Comparing equation 1 and equation 2, we get
⇒vt=(v−8)(t+3)
⇒vt=(v)(t+3)−8(t+3)=vt+3v−8t−24
cancel vt from both side
⇒0=3v−8t−24
⇒3v−8t=24
⇒3v=24+8t
⇒v=24+8t3
but from equation 1 the value of t=Sv=480v(hour)
⇒3v=24+8(480v)
⇒3v2=24v+3840
⇒3v2−24v−3840=0
⇒v2−8v−1280=0
factorize the quadratic equation
⇒(v−40)(v+32)=0
v is either 40kmh or −32kmh
Speed is Positive hence
Speed=40km/h
HOPE YOU ARE ABLE TO UNDERSTAND
Explanation:
Total Distance S=480km
Formula For Speed
speed=distancetime
Hence distance=speed×time
Case-I
let the uniform speed of Train =vkmh
and the time taken to complete distance =(t)hour
Distance S=speed×time=vt -(equation 1)
Case-II
If speed has been 8km/h less then train would have taken 3 hours more to cover the same distance.
Now in this situation
speed of train =(v−8)kmh
and Time taken to complete distance =(t+3)hour
Distance S=speed×time=(v−8)(t+3) - (equation 2)
Since Distance for both cases are same .
Comparing equation 1 and equation 2, we get
⇒vt=(v−8)(t+3)
⇒vt=(v)(t+3)−8(t+3)=vt+3v−8t−24
cancel vt from both side
⇒0=3v−8t−24
⇒3v−8t=24
⇒3v=24+8t
⇒v=24+8t3
but from equation 1 the value of t=Sv=480v(hour)
⇒3v=24+8(480v)
⇒3v2=24v+3840
⇒3v2−24v−3840=0
⇒v2−8v−1280=0
factorize the quadratic equation
⇒(v−40)(v+32)=0
v is either 40kmh or −32kmh
Speed is Positive hence
Speed=40km/h
HOPE YOU ARE ABLE TO UNDERSTAND
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
|
|
Top Courses for Class 10View all
A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula?
Question Description
A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? 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 uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? 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 uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula?.
A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? 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 uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? 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 uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula?.
Solutions for A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? 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 uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? defined & explained in the simplest way possible. Besides giving the explanation of
A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula?, a detailed solution for A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? has been provided alongside types of A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? theory, EduRev gives you an
ample number of questions to practice A train travels a distance of 480 km at uniform speed.If the speed had been 8km/h less,then it would have taken 3 hours more to cover the same distance. W need to find the speed of the train. Related: Using Quadratic Formula? 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