Question

A train travels 360 km at a uniform speed.
If the speed had been 5km/h more it
would have taken 1 hour less for the same
journey. Find the quadratic equation to
find the speed of train.​

Answer 1

Given distance=360 km.

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

Speed when increased by 5 km/hr =(x+5) km/hr

x

x360 − (x+5)36 =1

[360x+1800−360x] =1

x(x+5)

x 2

+5x−1800=0

x ² +45x−40x−1800=0

x ²+45x−40x−1800=0

+45x−40x−1800=0x(x+45)−40(x+45)=0

+45x−40x−1800=0x(x+45)−40(x+45)=0(x−40)(x+45)=0

+45x−40x−1800=0x(x+45)−40(x+45)=0(x−40)(x+45)=0x=40,−45

+45x−40x−1800=0x(x+45)−40(x+45)=0(x−40)(x+45)=0x=40,−45The speed of the train is 40 km/hr.

Answer 2

Consider the given question,

Distance =360 km

Speed =x km/hr

When speed is increase (x+5) km/hr

Given expression is written as,

⇒ 360 / x − 360 /(x+5) =1

⇒ ,x+5−x / x(x+5) = 1/ 360

⇒x²+5x=1800

⇒x ² +5x−1800=0

⇒x ² +45x−40x−1800=0

⇒x(x+45)−40(x+45)=0

⇒(x+45)(x−40)=0

⇒x=40,−45

But, speed can not be negative.

Hence, speed is 40 km/h

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