A train travels at a certain average speed for a distance of 63 km. There after it travels a distance of 72 km with an average speed of 6 km/hour more than the original speed. Total time taken to complete the journey is 3 hours. What is the original average speed of the train?

Solution

We have to find the original average speed of the train. Total journey completed in 3 hours. We know, distance = speed/me Given, that a train travels a distance of 63km at an average speed of x km/hr, Time = 63/x Given, that the same train travels a distance of 72km at an average speed of (x+6)km/hr, Time = 72/(x+6) So, 3 = (63/x) + 72/(x+6) Dividing by 3 to both sides, 1 = 21/x + 24/(x+6) x (x + 6) = 21(x + 6) + 24(x) x² + 6x = 21x + 126 + 24x By grouping, x² + 6x - 21x - 24x = 126 x² - 39x - 126 = 0 x² - 42x + 3x - 126 = 0 x (x - 42) + 3(x - 42) = 0 (x - 42)*(x + 3) = 0 Now, x - 42 = 0 x = 42 Also, x + 3 = 0 x = -3 Since the average speed x cannot be negative, So, x = 42km/hr