Question

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

Options

• 42 km/hr

• 44 km/hr

• 46 km/hr 

• 48 km/hr

Answer 1

42 km/hr

Explanation:

Let the original speed be x,

Then according to question

`63/"x" + 72/("x" + 6)` = 3

⇒ `21/"x" + 24/("x" + 6)` = 1

⇒ `(21("x" + 6) + 24"x")/("x"("x" + 6))` = 1

⇒ 21x + 126 + 24x = x² + 6x

⇒ x² – 39x – 126 = 0

⇒ x² – (42 – 3)x – 126 = 0

⇒ x² – 42x + 3x – 126 = 0

⇒ x(x – 42) + 3(x – 42) = 0

⇒ (x + 3) (x – 42) = 0

This gives x = –3 and x = 42

Since speed cannot be negative, so we ignore –3,

Therefore original average speed is 42 km/hr.