Question
Two trains, each 100 meters long, are running in
opposite directions. If one train's speed is twice that of the other and they take 10 seconds to cross each other, find the speed of the slower train.Solution
ATQ, Total distance travelled by the trains = 100 + 100 = 200 meters = (200/1000) km = 0.2 km Time taken = (10/3600) hours Let the speed of the slower train be ‘x’ km/hr Speed of the faster train = 2x km/hr Their relative speed = (2x + x) = 3x km/hr According to the question, 
Therefore, the speed of the slower train = 24 km/hr.
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 103x² - 470x + 367 = 0
Equation 2: 107y² - 504y + 397 = 0
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Equation 1: x² - 36x + 288 = 0
Equation 2: y² - 36y + 320 = 0
In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y.
I. x
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I. 2x² - 15x + 27 = 0
II. 2y² - 13y + 20 = 0
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Equation 2: y² - 29y + 210 = 0
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