A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

Let the speed of stream be x km/h

Speed of boat is 18 km/hr

Speed downstream = (18 + x)km/h

Speed upstream = (18 – x)km/h

{ using (a + b)(a – b) = a^{2} – b^{2} }

324 – x^{2} = 48x

x^{2} + 48x – 324 = 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 = 1 b = 48 c = – 324

= 1. – 324 = – 324

And either of their sum or difference = b

= 48

Thus the two terms are 54 and – 6

Difference = 54 – 6 = 48

Product = 54. – 6 = – 324

x^{2} + 54x – 6x – 324 = 0

x(x + 54) – 6(x + 54) = 0

(x + 54)(x – 6) = 0

x = – 54 or x = 6

(but x cannot be negative)

x = 6

Hence the speed of stream is 6 km/h

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