Question

A man can row $30km$ upstream and $44km$ downstream in $10$ hours. He can also row $40km$ upstream and $55km$ downstream in $13$ hours. Find the rate of current.

• A. $3km/h$
• B. $2km/h$
• C. $4km/h$
• D. $5km/h$

Answer 1

The correct option is A $3km/h$

Let a be the rate upstream

and b be the rate down stream

Therefore,

$\frac{40}{a}+\frac{55}{b}=13$

and $\frac{30}{a}+\frac{44}{b}=10$

Multiply equation $y$ by $4$ and equation $x$ by $3$ and subtracting.

$\frac{11}{b}=10orb=11$

putting the value $b$$=$$11$ in equation $x$

$a$ $=$ $5$

rate in still water $=$ $\frac{1}{2}\left(11+5\right)=8km/h$

rate of current $=\frac{1}{2}\left(11-5\right)$

$=3km/h$