# The speed of a bo

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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