Question

passenger 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 its usual speed​

Answer 1

SOLUTION

Let the distance of the train =x km/hr

Total distance= 300km

Time taken= 300/x hrs.......(1)

New speed of train = (x+5)km/hr

Time taken = 300/(x+5)hrs...........(2)

A/q

=) 300/x - 300/x+5 = 2 (from (1) &(2)

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

=) 1500= 2x^2 +10x

=) 2x^2 +10x - 1500=0

=) x^2 +5x -750= 0

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

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

=)x= -30 or x= 25

=) -30 (reject)

usual speed of train = 25 km/hrs.

Hope it helps ✔️

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 .