Discussion Forum

A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in $6 \frac{1}{2}$ hours. The velocity of the current is :

Answer:

Explanation:

Let rate upstream $=x$ kmph and rate downstream $=y$ kmph.

Then, $\frac{24}{x}+\frac{36}{y}$ $=6$ ....(i)

and $\frac{36}{x}+\frac{24}{y}$ $=\frac{13}{2}$ ...(ii)

Adding (i) and (ii), we get : $60\left(\frac{1}{x}+\frac{1}{y}\right)$ $=\frac{25}{2}$

or $\frac{1}{x}+\frac{1}{y}$ $=\frac{5}{24}$ ....iii)

Subtracting (i) from (ii), we get : $12\left(\frac{1}{x}-\frac{1}{y}\right)$ $=\frac{1}{2}$

or $\frac{1}{x}-\frac{1}{y}$ $=\frac{1}{24}$ .....iv)

Adding (iii) and (iv), we get : $\frac{2}{x}$ $=\frac{6}{24}$ or $x=8$

So $\frac{1}{8}+\frac{1}{y}$ $=\frac{5}{24}$

$\frac{1}{y}$ $=\frac{5}{24}-\frac{1}{8}$ $=\frac{1}{12}$ $\Leftrightarrow y=12$

Speed upstream = 8 kmph, Speed downstream = 12 kmph.

Hence, rate of current $= \frac{1}{2}(12-8)$ kmph = 2 kmph.