Question

Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

• A. (6,4)
• B. (4,6)
• C. (8,12)
• D. (12,8)

Answer 1

The correct option is A (6,4)

Let the speed of the boat in still water be $x\frac{km}{hr}$ and speed of the stream be $y\frac{km}{hr}$.

Then the speed of the boat downstream = $(x+y)\frac{km}{hr}$,

The speed of the boat upstream = $(x–y)\frac{km}{hr}$

Also, $Speed=\frac{\left(distance\right)}{\left(time\right)}$

In first case Ritu covers a distance of 20 Km downstream in 2 hours

$\therefore x+y=\frac{20}{2}$

$\Rightarrow x+y=10$.....(1)

In the other case Ritu covers a distance of 4 km upstream in 2 hours

$\therefore x-y=\frac{4}{2}$

$\Rightarrow x-y=2$.....(2)

Solving the equations by elimination method.

Adding (1) and (2) we get $2x=12\Rightarrow x=6$

Substituting in one of the equation we get $6+y=10\Rightarrow y=4$

Hence speed of rowing in still water is $6\frac{km}{hr}$ and the speed of the current is $4\frac{km}{hr}$.