Q. 184.2( 9 Votes )

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Answer :

Given: Speed of boat = 18 km/h


Distance = 24 km


To find: speed of the stream


Method Used:


To solve the quadratic equation by factorisation method, follow the steps:


1) Multiply the coefficient of x2 and constant term.


2) factorise the result obtained in step 1.


3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them


You get coefficient of x.



Explanation:


Given, motor boat whose speed in still water is 18 km/hr. takes 1 hour more to go 24 km up stream that to return downstream to the same spot.


Let the speed of stream be ‘a’ km/hr.


Relative speed of boat going upstream = 18 – a km/hr


Relative speed of boat going downstream = 18 + a km/hr



24(18 + a – 18 + a) = -a2 + 324


a2 + 48a – 324 = 0


a2 + 54a - 6a – 324 = 0


a (a + 54) – 6(a + 54) = 0


(a – 6) (a + 54) = 0


a = 6 and a = -54


As speed cannot be negative.


a = 6 km/hr.


Hence speed of the stream is 6 km/hr.


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