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Question

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

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Solution

let the usual speed of train be x km/hr,

Then the increased speed of the train is = (x + 5) km/hr

Time taken by the train under usual speed to cover 360km = 360 over x hr

Time taken by the train under increased speed to cover 360 km =fraction numerator 360 over denominator x plus 5 end fractionhr

Therefore,
360 over x � fraction numerator 360 over denominator left parenthesis x plus 5 right parenthesis end fraction equals 1
fraction numerator 360 left parenthesis x plus 5 right parenthesis � 360 x over denominator x left parenthesis x plus 5 right parenthesis end fraction equals 1
fraction numerator 360 x plus 1800 � 360 x over denominator x squared plus 5 x end fraction equals 1
1800 space equals space x squared space plus space 5 x space x squared space plus space 5 x space � space 1800 space equals space 0 space space x squared space � space 40 x space plus space 45 x space � space 1800 space equals space 0 space x left parenthesis x space � space 40 right parenthesis space plus space 45 left parenthesis x space � space 40 right parenthesis space equals space 0 space space left parenthesis x space plus space 45 right parenthesis left parenthesis x space � space 40 right parenthesis space equals space 0 space space x space equals space 40 space space o r space x space equals space � space 45

Since the speed of the train can never be negative

Hence, the original speed of the train is 40 km/hr.


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