Question

A train travels 360 km at a uniform speed if the speed had been 5 kilometre per hour more it would have taken 1 hour less for the same journey find the speed of the train

Answer 1

Distance=360 km
Let Speed=x km
Time=Distance/Speed
=360/x hours

If Speed is 5km/h more then time taken is 1 hour less
Speed=x+5 km/h
Time=360/x-1 hours
Distance=360 km/h

Then A/Q
Speed=Distance/Time
x+5=360/360/x-1
(x+5)(360/x-1)=360
(x+5)(360-x/x)=360 Taking x as Denominator)
(x+5)(360-x)=360x
360x-x²+1800-5x=360x
360x-x²+1800-5x-360x=0
0=x²+5x-1800

Now Factorize it by Middle term splitting
First Split 5x such that After Multiply We get 1800 and after subtract we get 5x

Then
x²+45x-40x-1800
X(X+45) -40(x+45)
Now Factors
(x-40) (x+45)=0

Now We get
x-40=0
x=40

X+45=0
x=-45

Speed=40 km/h

Answer 2

Answer:

DISTANCE = 360 KM ,

LET , SPEED = X

SO, 360/X -360/X+5 = 1

==> 360X + 1800 - 360X / X²+5X  = 1

==> 1800 = X²+5X

==> 0 = X²+5X-1800

==> 0 = X²+45X-40X-1800

==> 0 = X(X+45)-40(X+45)

==> (X+45) (X-40) = 0

==> X = -45 , 40

 SPEED = 40

BECAUSE -45 IS NOT POSSIBLE