A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/hour less than that of the fast train, find the speeds of the two trains.
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Let the speed of the slow train be x.
The speed of the fast train = x + 10
Time taken by slow train is :
600/x
Time taken by fast train is :
600/(x + 10)
This is 3 hrs less.
Equating the two we have :
600/(x + 10) + 3 = 600/x
600x +3x (x + 10) = 600(x + 10)
600x + 3x² + 30x = 600x + 6000
3x² + 30x - 6000 = 0
x² + 10x - 3000 = 0
x² + 60x - 50x - 3000 = 0
x(x + 60) - 50(x + 60) = 0
(x + 60)(x - 50) = 0
x = - 60 or 50
We take positive value since speed is positive.
The speed of the slowest train is 50km/h
The speed of the fastest train is 50 + 10 = 60km/h
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