Question

A train travel at this at an average speed for a distance of 63 km and then the travel that distance of 72 km at an average speed of 6 km/h more than its original speed if it takes three hours to complete total journey what is the original average speed

Answer 1

★ SPEED, DISTANCE & TIME ★

Given that Distance $= 63 km$

Let Original Speed of Train $= x km/hr$

$Time = \frac{ Distance}{Speed} = \frac{63}{x} hrs$

So, It travels a distance of 72 km at a average speed of 6 km/hr more than the original speed.

Now, $Distance = 72 km$
And, $Speed = (x + 6) km/hr$

∴ $Time = \frac{72}{(x+6)} hrs$

If it takes 3 hours to complete the whole journey, 

Then, $\frac{63}{x} + \frac{72}{(x + 6)} = 3 hrs$

⇒ $63(x + 6) + 72x = 3x(x + 6)$

⇒ $21(x + 6) + 24x = x(x+6)$

⇒ $45x + 21 * 6 = x^{2} + 6x$

⇒ $x^{2}- 39x - 126 = 0$

⇒ $x^{2}- 39x - 126 = 0$

⇒ $(x - 42)(x + 3) = 0$

Thus, $x = 42 km/hr$

∴ The Original Average Speed $= 42 km/hr$