A man rows to a place 48 km distant and come back in 14 hours. He finds that he

Question

A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

Options:

A . 1 km/hr

B . 1.5 km/hr

C . 2 km/hr

D . 2.5 km/hr

Answer: Option A

Suppose he move 4 km downstream in x hours. Then,

Speed downstream = \(\left(\frac{4}{x}\right)\) km/hr

Speed upstream = \(\left(\frac{3}{x}\right)\) km/hr

So, \(\frac{48}{(\frac{4}{x})} + \frac{48}{(\frac{3}{x})}= 14 or x=\frac{1}{2}\)

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

Rate of the stream = \(\frac{1}{2}\) (8 - 6) km/hr = 1 km/hr

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