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A train travels at a certain average speed for a distance 630 kilometre and then travels a distance of |
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Answer» Answer: Given that distance = 63 km. Let original speed of train = x km/hr. time = distance / time = 63/x hrs. And it travels a distance of 72 km at a average speed of 6 km/hr more than the original speed. distance = 72 km ; speed = (x + 6) km/hr . time = 72/(x+6) hrs. If it takes 3 hours to complete the WHOLE journey 63/x + 72/(x + 6) = 3 hrs ⇒ 63(x + 6) + 72X = 3x(x + 6) ⇒ 21(x + 6) + 24x = x(x+6) ⇒ 45X + 21×6 = x2 + 6x ⇒ x2 - 39X - 126 = 0 ⇒ x2 - 39x - 126 = 0 ⇒ (x - 42)(x + 3) = 0 ∴ x = 42 km/hr ∴ the original average speed = 42 km/hr
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