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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.
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