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Ex 4.3, 8 - A train travels 360 km at a uniform speed. - Ex 4.3

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Ex 4.3 ,8 A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train. Let the speed of train be x km/hr From (1) (x + 5) (360/๐‘ฅ " โ€“ 1" ) = 360 (x + 5) ((360 โˆ’ ๐‘ฅ)/๐‘ฅ) = 360 (x + 5) (360 โ€“ x ) = 360x x(360 โ€“ x) + 5(360 โ€“ x ) = 360 x 360x โ€“ x2 +5(360) โ€“ 5x = 360 x 360x โ€“ x2 + 1800 โ€“ 5x = 360 x 360x โ€“ x2 + 1800 โ€“ 5x โ€“ 360 x = 0 โ€“ x2 โ€“ 5x โ€“ 360 x + 360x + 1800 = 0 โ€“ x2 โ€“ 5x + 1800 = 0 0 = x2 + 5x โ€“ 1800 x2 + 5x โ€“ 1800 = 0 We factorize by splitting the middle term method x2 + 45x โ€“ 40x โ€“ 1800 = 0 x (x + 45) โ€“ 40 (x + 45) = 0 (x + 45) (x โ€“ 40) = 0 Hence x = โ€“ 45, x = 40 are the roots of the equation We know that Speed of train = x So, x cannot be negative โˆด x = 40 is the solution So, Speed of train = x = 40 km/hr

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