default_background
✕

Find the best tutors and institutes for Class 10 Tuition

Find Best Class 10 Tuition

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

Q2(iv):
Represent the following situations in the form of quadratic equations : (iv) A train travels a distance of $480$ km at a 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 :

Given:

  • Total distance to be covered by the train, $d = 480$ km.
  • The train travels at a uniform speed.
  • If the speed were $8$ km/h less, the time taken to cover the same distance would increase by $3$ hours.

To Find:

Represent the given situation in the form of a quadratic equation in terms of the speed of the train.

Step 1: Defining Variables

Let the uniform speed of the train be $x$ km/h.

We know the fundamental relationship between distance, speed, and time is given by the formula:

$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Step 2: Formulating Time Expressions

Case 1: When the train travels at the original uniform speed $x$ km/h.

Time taken ($t_1$) = $\frac{480}{x}$ hours.

Case 2: When the speed is reduced by $8$ km/h.

New speed = $(x - 8)$ km/h.

Time taken ($t_2$) = $\frac{480}{x - 8}$ hours.

Step 3: Establishing the Relationship

According to the problem, the train takes $3$ hours more when the speed is reduced. Therefore, the difference between the new time ($t_2$) and the original time ($t_1$) is $3$ hours:

$t_2 - t_1 = 3$

Substituting the expressions from Step 2:

$\frac{480}{x - 8} - \frac{480}{x} = 3$

Step 4: Simplifying the Equation

Divide the entire equation by $3$ to simplify the coefficients:

$\frac{160}{x - 8} - \frac{160}{x} = 1$

Find a common denominator for the left-hand side, which is $x(x - 8)$:

$\frac{160x - 160(x - 8)}{x(x - 8)} = 1$

Expand the numerator:

$\frac{160x - 160x + 1280}{x^2 - 8x} = 1$

Simplify the numerator ($160x - 160x = 0$):

$\frac{1280}{x^2 - 8x} = 1$

Step 5: Final Algebraic Form

Multiply both sides by $(x^2 - 8x)$:

$1280 = x^2 - 8x$

Rearrange the terms to the standard form of a quadratic equation $ax^2 + bx + c = 0$:

$x^2 - 8x - 1280 = 0$

Final Answer: The quadratic equation representing the situation is $x^2 - 8x - 1280 = 0$, where $x$ is the speed of the train in km/h.


More Questions from Class 10 Mathematics Quadratic Equations EXERCISE 4.1


CBSE Solutions for Class 10 Mathematics Quadratic Equations


Chapters in CBSE - Class 10 Mathematics


Top Tutors who teach Quadratic Equations

locationImg Govindpuram, Ghaziabad
experience 20 yrs of Exp students 1 student
greenClock 34 hrs of classes completed
Maths teacher for last 15 years
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

I teach mathematics and science for class 10th students. In science I teach physics chemistry and biology. My aim is to teach the students in way so that they score 100percent in boards.

Skills: Mathematics , Science
Also teaches: Class 11 Tuition, Class 8 Tuition and more

Zakir Hussain Class 10 Tuition trainer in Patna
(24)
Top Tutor
locationImg Alamganj, Patna
experience 4 yrs of Exp students 9 students
greenClock 16 hrs of classes completed
rsIcon 200 per hour
Expert Mathematics Trainer With 4 Years Experience @150/ hour
homeTutions Student's Home
regularClasses Tutor's home

I am teaching in school ( Dalimss Sunbeam school Ghazipur ) as a PGT teacher.. I have over all 4 years experience in this field.

Anamika

He is a very thoughtful teacher who puts a lot of thought into how he presents the material his lessons were engaging, useful and he was very patient with everyone in class always encouraging to students.

Skills: Mathematics
Also teaches: BTech Tuition, Class I-V Tuition and more

(52)
Top Tutor
locationImg Karampura, Delhi
experience 10 yrs of Exp
rsIcon 2500 per hour
Tutor
Online Classes Online Classes
homeTutions Student's Home

I am an IIM Kashipur alumnus, passionate about guiding students to achieve their immediate and long-term goals. As a personal tutor and founder of the online educational startup ‘MinDely,’ I have gained deep insights into child psychology and student needs, allowing me to tailor my teaching methods accordingly. I design lesson plans based on each student's grasp of concepts, ensuring a student-friendly and easy-to-understand approach. My weekly tests provide valuable insights for parents to track their child’s progress. I take pride in the success of my students, many of whom have graduated from IITs, DTU, and NSIT.

Vandit Sharma

Mr. Prabhjee Bhatia is an excellent teacher with some mind boggling teaching skills. He helped me to score excellent marks in all the exams of this year, can't thank him enough.

Skills: Mathematics , Science
Also teaches: Class 9 Tuition, Class 12 Tuition and more

(22)
Top Tutor
locationImg Ayodhya Nagar, Vijayawada
experience 5 yrs of Exp students 1 student
greenClock 715 hrs of classes completed
rsIcon 470 per hour
"Empowering students to reach for the stars."
Online Classes Online Classes

I am an experienced educator with 8 years of teaching and training expertise, specializing in all subjects for students from Class 1 to 8 across various academic boards. Additionally, I offer professional Microsoft Excel training (basic to advanced), designed to equip learners with practical skills for academic and professional use. I hold a B.Tech in Information Technology, which has strengthened my analytical and technical foundation, enabling me to integrate practical and modern methods into my teaching. Over the past 8 years, I have worked with students from diverse backgrounds and learning levels, ensuring that every learner gets individual attention and a personalized learning experience. I strongly believe in active communication with both students and parents, addressing concerns and adapting methods to suit each child’s unique pace and goals. One of my proudest achievements is the academic success of my students—for instance, 8 out of 10 students recently scored 95+ in Mathematics under my guidance. I was also recognized as a Star Tutor for 6 consecutive months at Filo EdTech, based on session quality, student feedback, and consistent results, which reflects my dedication to quality education. I conduct only online classes for flexible and convenient learning. My teaching approach is structured yet interactive, ensuring clarity and engagement through the following steps: Concept Explanation: Breaking down topics into simple, easy-to-understand concepts. Interactive Sessions: Encouraging students to ask questions and clarify doubts during class. Practice Work: Providing assignments and exercises for reinforcement. Progress Tracking: Offering regular feedback and performance assessments. For Microsoft Excel training, I follow a practical-based approach, using real-life examples and hands-on exercises, so learners can immediately apply their knowledge. I make use of PowerPoint presentations, digital whiteboards, and provide notes when required to ensure an effective and engaging learning experience.

Skills: Mathematics
Also teaches: Class I-V Tuition, Class 6 Tuition and more

(7)
Top Tutor
locationImg Kushaiguda, Hyderabad
experience 13 yrs of Exp students 1 student
greenClock 126 hrs of classes completed
rsIcon 300 per hour
Physics teacher with 15 years experience in Hyderabad 10 from reputated Corporate institution
Online Classes Online Classes
homeTutions Student's Home

Teaching is my passion I am into teaching profession since 16 years. I like challenges with young minds.. I will make students to confident by explaining concepts, taking special care. Cent percent assurance to child growth, committed to work towards target. I used to counsel the students to succeed in their exams.

M.shivakumar

Good teaching sir. It is very helpful for me subject wise very good and teaching wise also very good sir.

Skills: Mathematics , Science and more

Find more Tutor for Quadratic Equations in your City


Other Subjects in CBSE - Class 10

Worksheet Icon

Download free CBSE - Class 10 Mathematics Quadratic Equations EXERCISE 4.1 worksheets

Download Now

Find Best Class 10 Tuition ?

Find Now »