Question

A train travel 180 km of uniform speed if the speed had been 6 km/ hr more it would have taken 1 hr less for the same journey

Answer 1

Let the speed of train be x km /h
Distance = 180 km
So, time = 180 / x
When speed is 9 km/h more, time taken = 180 / x+9 
According to the given information:
180 / x - 180 / x+9 = 1
180 (x+9-x) / x(x+9) = 1
180 * 9 = x(x+9)
1620 = x2 + 9x 
x2 + 9x - 1620 = 0
x2 + 45x - 36x - 1620 = 0 
x(x+45) - 36(x+45) = 0
(x-36)(x+45) = 0
x = 36 or -45
But x being speed cannot be negative.
So, x = 36
Hence, the speed of the train is 36km/h.