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Question

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.

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Solution

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.
360x360x+5=4860
Dividing both sides by 360, we get
1x1x+5=4860×360
x+5x(x+5)(x)=1450
5x2+5x=1450
x2+5x=2250
x2+5x2250=0
x245x+50x2250=0
x(x45)+50(x45)=0
(x45)(x+50)=0
x=45,50
Since, speed can't be a negative quantity.
Therefore, required speed of the train is =45 km/hr.


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