A train, travelling at a uniform speed for 360km, 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 = 360km

We know that,

$begin mathsize 12px style s p e e d space equals space fraction numerator d i s tan c e space over denominator t i m e end fraction therefore space t i m e space equals space fraction numerator d i s tan c e over denominator t i m e end fraction end style$

Time take by the train intially =

If the speed was increased by 5km/hr

Time taken by train = $begin mathsize 12px style fraction numerator 360 over denominator x plus 5 end fraction end style$

Difference in the time taken is 48 minutes,

$begin mathsize 12px style fraction numerator 360 over denominator x space end fraction minus space fraction numerator 360 over denominator x plus 5 end fraction space equals space 48 over 60 space space space space space left parenthesis c o n v e r t i n g space 48 m i n s space t o space h o u r s right parenthesis rightwards double arrow 360 open square brackets fraction numerator x plus 5 minus x over denominator x left parenthesis x plus 5 right parenthesis end fraction close square brackets equals 4 over 5 rightwards double arrow 90 open square brackets fraction numerator 5 over denominator x left parenthesis x plus 5 right parenthesis end fraction close square brackets equals 1 fifth rightwards double arrow 90 left square bracket 5 right square bracket 5 equals x squared plus 5 x end style$

x=45,-50
Speed = 45 km/hr as speed cannot be negative

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A train, travelling at a uniform speed for 360km, 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 = 360km We know that, Time take by the train intially = If the speed was increased by 5km/hr Time taken by train = Difference in the time taken is 48 minutes, x=45,-50 Speed = 45 km/hr as speed cannot be negative