Case 4_ Two Trains Crossing One Other (Same Direction)

Duration: 13 min

This video lesson is available to enrolled students.

Enroll to watch — TCS SuperSet Course

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive tutorial on solving "Train Problems," specifically focusing on "Case 4: Two Trains Moving In Same Direction." Presented by Yash Jain from Knowledge Gate Eduventures, the lecture begins by establishing the fundamental concepts of relative speed and total distance required for trains to cross each other. The instructor systematically works through three distinct numerical examples, demonstrating the step-by-step application of formulas, unit conversions between kilometers per hour and meters per second, and algebraic manipulation to find unknown variables such as time, length, and speed. The visual aids include on-screen text of the problems, handwritten calculations on a digital whiteboard, and diagrams illustrating train movements. The lesson is structured to take students from basic understanding to advanced problem-solving techniques, ensuring clarity in each step of the mathematical process.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an introductory title card reading "PROBLEM ON TRAINS" and "Basic To Advance" by Yash Jain. It transitions to a slide titled "Case 4: Two Trains Moving In Same Direction," decorated with rocket and planet icons. The instructor explains the concept of relative speed when two objects move in the same direction, drawing arrows to indicate direction and writing "diff" to signify that the relative speed is the difference between the two speeds. He introduces the basic formula S = d/t (Speed = Distance / Time) as the foundation for solving these problems. He emphasizes that for trains moving in the same direction, the relative speed is calculated by subtracting the slower speed from the faster speed, a key distinction from opposite direction problems.

  2. 2:00 – 5:00 02:00-05:00

    The first numerical problem is introduced: "Two trains Bangalore Rajdhani (length 80 meters) and Gondwana Express (length 100 meters) are moving on parallel tracks in the same direction with speeds 90 kmph and 60 kmph. Find the time (in seconds) in which Bangalore Rajdhani will cross Gondwana Express completely." The instructor underlines the key values and calculates the relative speed as 90 - 60 = 30 kmph. He converts this to meters per second using the factor 5/18, resulting in 25/3 m/s. He then calculates the total distance as the sum of lengths (80 + 100 = 180 meters). Finally, he applies the formula t = d/s to find the time, resulting in 21.6 seconds. He writes out the calculation t = 180 / (25/3) = 180 x 3 / 25 = 108/5 = 21.6 sec on the board, showing the intermediate steps clearly.

  3. 5:00 – 10:00 05:00-10:00

    The second problem involves "Patalkot Express and Shreedham Express" moving in the same direction with speeds of 72 km/hr and 54 km/hr. They cross each other in 20 seconds, and the length of the faster train is 40 meters. The goal is to find the length of the slower train. The instructor converts the speeds to m/s (20 m/s and 15 m/s) and determines the relative speed is 5 m/s. He sets up the equation 5 = (40 + x) / 20, where x is the unknown length. Solving this, he finds the length of the slower train to be 60 meters. He writes the conversion steps clearly on the board, showing 72 x 5/18 = 20 and 54 x 5/18 = 15. An image of a train station sign reading "Shree Dham Jabalpur" is visible, adding context to the problem.

  4. 10:00 – 13:03 10:00-13:03

    The final problem features "Kaleen Express and Guddu Express" with lengths of 65 meters and 105 meters respectively. They cross each other in 51/2 seconds, and the speed of Kaleen Express is 84 kmph. The task is to find the speed of Guddu Express. The instructor calculates the total distance (170 meters) and the relative speed in m/s (20/3 m/s). He converts this relative speed to kmph (24 kmph). Using the relationship |84 - S2| = 24, he solves for the speed of Guddu Express, determining it to be 60 kmph. He writes the conversion from m/s to kmph as multiplying by 18/5. The instructor circles the final answer of 60 kmph to highlight the solution.

The video effectively guides students through the logic of relative motion for trains moving in the same direction. By breaking down the process into identifying given values, calculating relative speed (difference of speeds), summing the lengths for total distance, and applying the time-speed-distance formula, the instructor provides a clear methodology. The progression from finding time to finding length and finally finding speed demonstrates the versatility of the core concepts. The consistent use of unit conversion (5/18 factor) is emphasized as a critical step for accuracy in these problems. The instructor's handwritten notes on the digital whiteboard serve as a visual guide for students to follow along with the calculations, ensuring they understand the derivation of each result.