Question

Formulate the following problems as a pair of equations, and hence find their solutions:

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

Answer 1

Step 1: Formulate the equations

Let us assume that

Speed of Ritu in still water $=xkm/hr$

Speed of Stream $=ykm/hr$

Now, the speed of Ritu during,

Downstream $=x+ykm/h$

Upstream $=x–ykm/h$

As per the given conditions

$2(x+y)=20$

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

And, $2(x-y)=4$

$\Rightarrow$$x–y=2\dots \dots \dots \dots \dots \dots \dots \dots \dots \left(2\right)$

Step 2: Find their solution

By adding both the equations we get

$x+y+x-y=10+2$

$\Rightarrow$ $2x=12$

$\Rightarrow$ $x=6$

Substituting the value of $x=6$ in equation $\left(2\right)$, we get,

$6-y=2$

$\Rightarrow$$y=4$

Hence, the speed of Ritu rowing in still water is $6km/hr$ and the speed of the stream is $4km/hr$.