Question

A train travels at a certain speed for a distance of 63 km and then Travels a distance of 72 km at an average speed of 6 km per hour more than its original speed it takes 3 hours to complete total journey what is the original speed

Answer 1

Answer:

42 km/hr

Step-by-step explanation:

Given that  distance = 63 km.

Let original speed of train = x km/hr.

Formula : time = distance / speed =  63/x hrs.

And it travels a distance of 72 km at a average speed of 6 km/hr more than the original speed.

Since new speed is 6 km/hr more than the original speed.

So, new speed = x+6

Distance = 72 km ; speed = (x + 6) km/hr .

So, time = 72/(x+6) hrs.

If it takes 3 hours to complete the whole journey

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

⇒ 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

Hence the original average speed = 42 km/hr