Question

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

Answer 1

Let the speed = x km/h. Distance = 360km

then time taken = distance/speed
t1=360/x
if speed is increased by 5 km/h
speed will be (x+5)km/h  and distance is the same
t2= 360/(x+5)
time with original speed - time with increased speed = 1 

i.e. t1 -t2 = 1
360/x - 360/(x+5)=1
LCM= x(x+5)
(360(x+5)-360x) /x(x+5)=1
360x+1800-360x=x(x+5)
x²+5x = 1800
x²+5x-1800=0
x²+45x-40x-1800=0
x(x+45)-40(x+45)=0
(x-40)(x+45)=0
x= 40 km/h will be the original speed. (since, speed can't be negative and hence, can't be equal to -45km/h)