Question

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

Answer 1

300 / (x + 5) + 2 = 300 / x  

. . . combine left side into a single fraction  

(310 + 2x) / (x + 5) = 300 / x  

. . . cross multiply  

310x + 2x^2 = 300x + 1500  

2x^2 + 10x - 1500 = 0  

x^2 + 5x - 750 = 0  

(x - 25) (x + 30) = 0  

x = -30 <== invalid negative time  

x = 25 km / h <===== answer

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 .