A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed ?

Answer

Let the original average speed of train be x km/hr. Therefore,

$$ \frac{63}{x} + \frac{72}{x + 6} = 3 $$

x² - 39x - 126 = 0

(x - 42)(x + 3) = 0

$$ x \ne -3 $$

x = 42

Original speed of train is 42 km/hr.