A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more. Find the original speed of the train.
Let the speed of train be x km/hr
Distance to be travelled =360 km
Since,Speed=distancetime
⇒ time=Distancespeed
Time for cover 360 km with speed x km/hr is 360x hr.....(i)
In case if the speed is 5 km/hr is more then the time required to cover the same distance of 360 km is 360x+5 hr.....(ii)
Then times difference between (i) and (ii) is 48min=4860 hr.
⇒360x−360x+5=4860
Dividing both sides by 360, we get
⇒1x−1x+5=4860×360
⇒x+5−x(x+5)(x)=1450
⇒5x2+5x=1450
⇒x2+5x=2250
⇒x2+5x−2250=0
⇒x2−45x+50x−2250=0
⇒x(x−45)+50(x−45)=0
⇒(x−45)(x+50)=0
x=45,−50
Since, speed can't be a negative quantity.
Therefore, required speed of the train is =45 km/hr.