A train travels 360 km at a uniform speed .if the speed had been 5 km/h more it would have taken 1hour less for the same journey
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Let the speed of the train be x.
The new speed is x + 5
The time taken before the speed is increased is :
360/x
The time taken after the speed is increased is
360/(x + 5)
This time is 1 hr less.
We equate these two as follows :
360/x = 360/(x + 5) + 1
360(x + 5) = 360x + x (x + 5)
360x + 1800 = 360x + x² + 5x
x² + 5x - 1800 = 0
x² + 45x - 40x - 1800 = 0
x ( x + 45) - 40(x + 45) = 0
(x + 45) (x - 40) = 0
x = - 45 or 40
We take the speed which is positive.
The speed of the train is thus 40km/h
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