Question

A man rows to a place 35 km in distant and back in 10 hours 30 minutes. He found that he could row 5 km with the stream in the same time as he can row 4 km against the stream. Find the rate of flow of the stream.:

• A. 1 km/hr
• B. 0.5 km/hr
• C. 0.75 km/hr
• D. 1.5 km/hr

Answer 1

Answer:

C. 0.75 km/hr

Speed of man in still water = x kmph.

Speed of current = y kmph

Rate downstream = (x + y) kmph

Rate upstream = (x – y) kmph

According to the question,

$\frac{5}{x+y}=\frac{4}{x-y}$

$5(x-y)=4(x+y)$

$5x-5y=4x+4y$

$x=9y$

again, $\frac{35}{x+y}+\frac{35}{x-y}=10\frac{1}{2}=\frac{21}{2}$

$\frac{35}{9y+y}+\frac{35}{9y-y}=\frac{21}{2}$

$\frac{5}{10y}+\frac{5}{8y}=\frac{3}{2}$

$\frac{1}{2y}+\frac{5}{8y}=\frac{3}{2}$

$\frac{1}{y}+\frac{5}{4y}=3$

$\frac{4+5}{4y}=3$

$9=3\times{4y}$

$y=\frac{3}{4}kmph$

$=0.75kmph$