A fast train takes one hour less than a slow train for a journey of 200km. If the speed of the slow train is 10km/hr less than that of the fast train, find the speed of the two trains.

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Solution

Let speed of fast train be x km/hr
speed of slower train = x - 10 km/hr

It is given that fast train takes 1 hr less than slower one in covering 200 km

$rightwards double arrow space 200 over x space equals space fraction numerator 200 over denominator x minus 10 end fraction minus 1 space rightwards double arrow space space 200 over x space equals space fraction numerator 200 minus left parenthesis x minus 10 right parenthesis over denominator x minus 10 end fraction rightwards double arrow space 200 over x space equals space fraction numerator 210 minus x over denominator x minus 10 end fraction rightwards double arrow 200 x minus 2000 space equals space 210 x space minus space x Â² space rightwards double arrow x Â² space minus space 10 x space minus space 2000 space equals space 0 space rightwards double arrow space x Â² space minus 50 x space plus space 40 x space minus 2000 space equals space 0 space space rightwards double arrow space left parenthesis x minus 50 right parenthesis left parenthesis x plus 40 right parenthesis space equals space 0 space x space equals space 50 space space a n d space x equals space minus space 40$

Since speed can't be negative, the speed of faster train = x = 50 km/hr
Speed of slower train = 40 km/hr

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A fast train takes one hour less than a slow train for a journey of 200km. If the speed of the slow train is 10km/hr less than that of the fast train, find the speed of the two trains.

Let speed of fast train be x km/hr speed of slower train = x - 10 km/hr It is given that fast train takes 1 hr less than slower one in covering 200 km Since speed can't be negative, the speed of faster train = x = 50 km/hr Speed of slower train = 40 km/hr