Q. 524.5( 4 Votes )

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Answer :

Let the speed of stream be x km/h

Speed of boat is 8 km/hr


Speed downstream = (8 + x)km/h


Speed upstream = (8 – x)km/h






296 – 7x = 320 – 5x2


5x2 – 7x – 24 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 5 b = – 7 c = – 24


= 5. – 24 = – 120


And either of their sum or difference = b


= – 7


Thus the two terms are 8 and – 15


Difference = 8 – 15 = – 7


Product = 8. – 15 = – 120


5x2 – 7x – 24 = 0


5x2 – 15x + 8x – 24 = 0


5x(x – 3) + 8(x – 3) = 0


(5x + 8)(x – 3) = 0


x = 3 or x = – 8/5


(but x cannot be negative)


x = 3


Hence the speed of stream is 3 km/hr


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