Question

A train travels 360km at auniform speed.If the speed had been 5km/h more,it would havce taken 1 hour less for the same journey.Find the speed of the train.Tell me the whole procedure

Answer 1

Let the speed of the train be x km/h
360/x
=>(360/x+5) + 1
=>360(x+5) = (360+x+5)x
=>360x+1800 = 360x+$x^{2}$+5x
=>$x^{2}$+5x-1800=0
By solving this equation the value of x is 40
Therefore the speed will be 40km/h

Answer 2

Distance = 360 km
Let the speed of the train be u  km/h
be the time taken to complete the journey be t₁ hr
so   
distance/speed = time
so     360/u = t₁  ............  ( i )

2nd case

the speed of the train (u + 5) km/h
so time taken  = t₁ - 1 hr

so 360/(u + 5) = t₁ - 1

substituting ( i ) in the equation

⇒$\frac{360}{u+5}=\frac{360}{u}-1$

⇒$\frac{360}{u+5}-\frac{360}{u}=-1$

⇒$\frac{360u-360u-1800}{u(u+5)}=-1$

⇒$\frac{1800}{u(u+5)}=1$   (cancelling the -1)

⇒$1800=u(u+5)$

⇒$1800=u^{2} +5u$

⇒$u^{2} +5u-1800=0$

⇒$u^{2} +45u-40u-1800=0$  (doing the middle term factor)

⇒$u(u+45)-40(u+45)=0$

⇒$(u-40)(u+45)=0$


so u = - 45 and 40 
so speed can't be negative so the the speed of the train is 40 km/hr