Question

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more,
have taken 1 hour less for the same journey. Find the speed of the train.
solve it by quadratic formula​

Answer 1

Answer:

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

We are given that 360 km distance is to be travelled at uniform speed of x km/hr.

Time taken to cover the distance of

360 km =

x

360

hours.

In case, the speed is increased by 5 km/hr, the time required to cover 360 km =

x+5

360

hours.

Now,

x

360

−

x+5

360

=1

⇒360×( x1

−

x+5

1

)=1

⇒

x×(x+5)

360×5

=1

⇒x×(x+5)=360×5

⇒x

2

+5x=1800

⇒x

2

+5x−1800=0

a=1,b=5,c=−1800

D=b

2

−4ac=(5)

2

−4×1×(−1800)

=25+7200=7225

⇒

D

=

7225

=85

Then x=

2a

−b±

D

=

2

−5±85

⇒x=

2

−5±85

or

2

−5−85

⇒x=40 or −45

We reject x=−45

Therefore, x=40