Question

a train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km per hour from its usual speed find the usual speed of the train

Answer 1

Answer:

Let the usual speed of the train be 'x' km/hr.

A.T.Q.

300/x – 300/(x+5) = 2

=> 300(x+5) – 300x / x(x+5) = 2

=> 300x + 1500 – 300x / x² + 5x = 2

=> 2(x² + 5x) = 1500

=> 2x² + 10x – 1500 = 0

=> x² + 5x – 750 = 0

=> x² + 30x – 25x – 750 = 0

=> x(x + 30) – 25 (x + 30) = 0

=> (x+30) (x–25) = 0

=> x = –30 or x = 25

Speed can't be negative. So, x = –30 is inappropriate.

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

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Hope my ans.'s satisfactory.☺

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 .