**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.

**Solution:**

Let the speed of rowing in still water be *x* km/hr and the speed of the current be *y *km/hr

Speed upstream $=(x-y) k n / h r$

Speed downstream $=(x+y) \mathrm{km} / \mathrm{hr}$

Now,

Time taken to cover $20 \mathrm{~km}$ down stream $=\frac{20}{x+y} h r s$

Time taken to cover $4 \mathrm{~km}$ upstream $=\frac{4}{x-y} h r s$

But, time taken to cover $20 \mathrm{~km}$ downstream in 2 hours

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

$20=2(x+y)$

$20=2 x+2 y \cdots(i)$

By solving these equation (i) and (ii) we get

Substitute $x=6$ in equation (i)we get

$2 x+2 y=20$

$12+2 y=20$

$2 y=20-12$

$2 y=8$

$y=\frac{8}{2}$

$y=4$

Hence, the speed of rowing in still water is $6 \mathrm{~km} / \mathrm{hr}$.

The speed of current is $4 \mathrm{~km} / \mathrm{hr} .4 \mathrm{~km} / \mathrm{hr}$

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