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(x^2+5x)` 

⇒`1500=2x^2+10x` 

⇒`x^2+5x-750=0` 

⇒`x^2+(30-25)x-750=0` 

⇒`x^2+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.