Question

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

Answer 1

HELLO DEAR,

let the usual speed be x
then the increase in speed is (x+5)

$- \frac{300}{x + 5} + \frac{300}{x} = 2 \\ = > \frac{ - 300x + 300x + 1500}{ {x}^{2} + 5x} = 2 \\ = > \frac{ 1500}{ {x}^{2} + 500x } = 2 \\ = > 1500 = 2 {x}^{2} + 10x \\ = > 2 {x}^{2} + 10x - 1500 = 0 \\ = > {x}^{2} + 5x + 750 \\ = > {x}^{2} + 30x - 25x - 750 = 0 \\ = > x(x + 30) - 25(x + 30) \\ = > (x - 25)(x + 30) \\ = > x = 25 \: or \: x = - 30$
I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Answer:

Let the usual speed of the train be y km / hr .

A.T.Q.

$\displaystyle{\frac{300}{y} -\frac{300}{y+5} =2 }$

300 ( y + 5 ) - 300 y = 2 y ( y + 5 )

y² + 5 y - 750 = 0

y² + 30 y - 25 y - 750 = 0

( y + 30 ( y -25 ) = 0

y = - 30 or y = 25

Since , speed of train can't be negative .

Therefore , the usual speed of the train is 25 km / hr .