Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

Let the speed of the stream be x km/h.
It is given that the speed of a boat in still water is 15 km/h.
Now,
Speed of the boat upstream = Speed of the boat in still water − Speed of the stream = (15 − x) km/h
Speed of the boat downstream = Speed of the boat in still water + Speed of the stream = (15 + x) km/h
We know that
Time=Distance/Speed
Time is taken for upstream journey + Time taken for the downstream journey = 4 h 30 min

$therefore space fraction numerator 30 over denominator 15 minus straight x end fraction space plus fraction numerator 30 over denominator 15 plus straight x end fraction space equals space 4 1 half rightwards double arrow space 30 open square brackets fraction numerator open parentheses 15 plus straight x close parentheses plus open parentheses 15 minus straight x close parentheses over denominator open parentheses 15 plus straight x close parentheses open parentheses 15 minus straight x close parentheses end fraction close square brackets space equals space 9 over 2 rightwards double arrow space 30 space open parentheses fraction numerator 30 over denominator 225 minus straight x squared end fraction close parentheses space equals space 9 over 2 rightwards double arrow space 225 minus straight x squared space equals space fraction numerator 30 space straight x 30 space straight x 2 over denominator 9 end fraction rightwards double arrow space 225 minus straight x squared space equals space 200 rightwards double arrow space straight x squared space equals space 225 minus 200 space equals space 25 rightwards double arrow space straight x space equals space plus-or-minus 5$

Since speed can not be negative, therefore, x = 5.
Thus, the speed of the stream is 5 km/h.

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