Question

A narrow gauge train takes 2 hour less for a journey of 300 km if its speed is increased by 5 km
normal speed.

Answer 1

Given:

Time taken = 2 hours less

Distance = 300km

Speed = +5km

To find:

The normal speed of the train

Solution:

Let the normal speed of the train be = x.

Therefore,

Time taken to cover 300 km = 300/x

Time taken with increased speed = 300/x + 5 hr

ATQ,

= 300/x + 300/(x + 5) = 2

= 300x + 1500 - 300x/x(x + 5) = 2

= 1500/x² + 5x = 2

= 1500 = 2x² + 10x

= x² + 5x - 750 = 0

Breaking the equation -

= x² + 30x - 25x - 750 = 0

= x(x + 30) - 25(x + 30) = 0

= (x + 30) (x - 25) = 0

x = - 30, and x = 25

As the value of x can not be negative, thus -

x = 25 km/h

Answer: The normal speed of the train is 25 km/h.

Answer 2

$\huge{\underline{\underline{\boxed{\sf{\purple{Answer࿐}}}}}}$

x = 25 km/h