Question

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

Answer 1

Ans is 25 km/hr
just to make a quadratic equation and its solved

Answer 2

Solution:
Let the usual speed be x km/hr.
Therefore, increased speed would be x+5 km/hr
Also let us say that it takes y hours to complete the journey @ x km/hr.

Then, According to the given conditions,
300/x = y .........E1
& 300/(x+5) = y - 2 ........E2
Substituting the value of y from E1 into E2, we get
300/(x+5) = (300/x) - 2
or 300/(x+5) = (300-2x)/x
or 300x = 300x - 2x^2 + 1500 - 10x
or 2x^2 + 10x = 1500
Dividing by 2,
x^2 + 5x = 750
x^2 + 5x - 750 = 0
Therefore, (x+30)(x-25)=0
Therefore, x= -30 or x = 25

Hence, the usual speed of the train is 25 km/hr