The distance between mumbai and pune is 192Km traveling by the Deccan Queen, it takes 48 Minutes less than another train. Calculate the speed of Deccan Queen if the speed of two trains differ by 20 Km/h
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Let the speed of deccan queen be x km/min
then the speed of other train is x-(1/3) km/min
Now, distance = speed × time
(192/(x-(1/3))) - (192/x) = 48
(1/3)/(x^2 - x/3) = 48 / 192 = 1/4
3x^2 - x - 4 = 0
3x^2 - 4x + 3x - 4 = 0
3x (x + 1) - 4 (x + 1) = 0
(3x - 4)(x + 1) = 0
x = 4/3 or -1
But x cannot be negative
So, x = 4/3 km/min = 80km/hr
then the speed of other train is x-(1/3) km/min
Now, distance = speed × time
(192/(x-(1/3))) - (192/x) = 48
(1/3)/(x^2 - x/3) = 48 / 192 = 1/4
3x^2 - x - 4 = 0
3x^2 - 4x + 3x - 4 = 0
3x (x + 1) - 4 (x + 1) = 0
(3x - 4)(x + 1) = 0
x = 4/3 or -1
But x cannot be negative
So, x = 4/3 km/min = 80km/hr
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answer is attached , speed of deccan queen will be 60 km/h
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