Question

a train travels a distance of 450km at uniform speed if the speed had been 8km/hr less than it would have taken 3hours more to cover the same distance find the speed of the train

Answer 1

Suppose the speed of the train is x km/h.
It takes 480x hours to travel, but if the speed were
8 km/h slower, it would take 480x−8 hours.

Now we've got the equation:
480x−8 = 480x +3
This can be solved as follows.

Multiple both sides of the equation by x(x−8). 
480x=480(x−8)+3x(x−8)

Deform and factorize the equation to solve it.
x2−8x−1280=0
(x−40)(x+32)=0
x=40,−32

Don't forget that the answer must be positive, so the speed
is x=40 km/h.

Let's check.
If we travel at 40 km/h, it takes 12 hours.
If we traveled at 32 km/h, it would take 15 hours, so the difference
is three hours and we've got the correct answer.
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