Question

A train travels 360km at unifom speed. If the speed had been 5km/hr. It would have taken 1 hr less for the same journey. Find the speed of the train

Answer 1

Let the speed of train be 's'
speed=(distance/time)
s=(d/t)
=>t=(d/s)

Here we've 2 cases of t
1st case
=> t=(360/s)
2nd case where the speed is increased by 5km/h
=>t= [360/(s+5)]

It would've been taken 1 hr less for the same journey if the speed had been 
5 km/hr more
=> 360/s-[360/(s+5)]=1
=>$\frac{360*(s+5)-(360*s)}{s(s+5)} =1 \\ \frac{360s+1800-360s}{s^2+5s}=1$
1800=s²+5s
=>s²+5s-1800=0
=>s²+45s-40s-1800=0
=>s(s+45)-40(s+45)=0
=(s+45)(s-40)=0
=>s=-45,40

Since the speed cannot be negative speed is 40 km/hr