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Question

A train, travelling at a uniform speed for360km, would have taken 48minutes less to travel the same distance if its speed were5km/h more. Find the original speed of the train.


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Solution

Step 1

Let the original speed of train=skm/h

We know that

Time=distancespeed

According to the question, we have,

Time is taken by train =360shour

And, Time taken by train its speed increase 5km/h=360/(s+5)

Step 2

Now, It is given that,

Time taken by train in first – time taken by train in 2nd case =48min=48/60hour

360/s360/(s+5)=48/60=4/5360(1/s1/(s+5))=4/5360×5/4(5/(s²+5s))=1450×5=s²+5ss²+5s-2250=0s=(-5±(25+9000))/2=(-5±(9025))/2=(-5±95)/2=-50,45Buts-50becausespeedcannotbenegativeSo,s=45km/h

Hence, original speed of train =45km/h


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