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      Question

      A car travels from town A to town B, a distance of 120

      km, at x km/h. It returns from B to A at (x + 20) km/h. The total time taken for the round trip is 5 hours. What is the value of x?
      A 60 km/h Correct Answer Incorrect Answer
      B 10 km/h Correct Answer Incorrect Answer
      C 40 km/h Correct Answer Incorrect Answer
      D 20 km/h Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Time A to B = 120/x Time B to A = 120/(x + 20) Total time = 5 hours: 120/x + 120/(x + 20) = 5 Divide by 5: 24/x + 24/(x + 20) = 1 Or multiply original equation: 120(x + 20) + 120x = 5x(x + 20) 120x + 2400 + 120x = 5x^2 + 100x 240x + 2400 = 5x^2 + 100x Rearrange: 5x^2 + 100x тИТ 240x тИТ 2400 = 0 5x^2 тИТ 140x тИТ 2400 = 0 Divide by 5: x^2 тИТ 28x тИТ 480 = 0 Discriminant D = 28┬▓ + 4├Ч480 = 784 + 1920 = 2704 = 52┬▓ x = (28 ┬▒ 52) / 2 Positive root = (28 + 52)/2 = 80/2 = 40 So x = 40 km/h.

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