Question

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.

Answer 1

Let the usual speed x km/hr.

According to the question:

`300/x - 300/(x + 5) = 0` 

⇒ `(300(x + 5) - 300x)/(x(x + 5)) = 2` 

⇒ `(300x + 1500 - 300x)/(x^2 + 5x) = 2` 

⇒ 1500 = 2(x² + 5x) 

⇒ 1500 = 2x² + 10x 

⇒ x² + 5x – 750 = 0 

⇒ x² + (30 – 25)x – 750 = 0 

⇒ x² + 30x – 25x – 750 = 0 

⇒ x(x + 30) – 25(x + 30) = 0 

⇒ (x + 30) (x – 25) = 0 

⇒ x = –30 or x = 25 

The usual speed cannot be negative; therefore, the speed is 25 km/hr.