# Sheila can row a boat 2 MPH in still water. How fast is the current of a river if she takes the same length of time to row 4 miles upstream as she does to row 10 miles downstream?

Jun 30, 2016

The speed of current of river is $\frac{6}{7}$ miles per hour.

#### Explanation:

Let the current of water be $x$ miles per hour and that Sheila takes $t$ hours for each way. As she can row a boat at $2$ miles per hour,

the speed of boat upstream will be $\left(2 - x\right)$ miles per hour and covers $4$ miles hence for upstream we will have

$\left(2 - x\right) \times t = 4$ or $t = \frac{4}{2 - x}$

and as the speed of boat downstream will be $\left(2 + x\right)$ miles per hour and covers $10$ miles hence for upstream we will have

$\left(2 + x\right) \times t = 10$ or $t = \frac{10}{2 + x}$

Hence $\frac{4}{2 - x} = \frac{10}{2 + x}$ or $8 + 4 x = 20 - 10 x$

or $14 x = 20 - 8 = 12$ and hence $x = \frac{12}{14} = \frac{6}{7}$ and $t = \frac{4}{2 - \frac{6}{7}} = \frac{4}{\frac{8}{7}} = 4 \times \frac{7}{8} = \frac{7}{2}$ hours.