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

Q2.    Formulate the following problems as a pair of equations, and hence find their solutions:
                (i) 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.

Answers (1)
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Let the speed of Ritu in still water be x and speed of current be y,

Let's solve this problem by using relative motion concept,

the relative speed when they are going in the same direction (downstream)= x +y 

the relative speed when they are going in the opposite direction (upstream)= x - y

Now, As we know,

Relative distance = Relative speed * time .

So, According to the question,

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

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

And,

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

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

Now, Adding (1) and (2), we get

2x=10+2

\Rightarrow 2x=12

\Rightarrow x=6

Putting this in (2)

6-y=2

\Rightarrow y=6-2

\Rightarrow y=4

Hence,

x=6\:and\:y=4.

Hence Speed of Ritu in still water is 6 km/hour and speed of the current is 4 km/hour

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