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?

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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?

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Answer 1 · 2016-06-30T16:56:07

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

Explanation:

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

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

$(2 - x) \times t = 4$ $(2-x)xxt=4$ or $t = \frac{4}{2 - x}$ $t=4/(2-x)$

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

$(2 + x) \times t = 10$ $(2+x)xxt=10$ or $t = \frac{10}{2 + x}$ $t=10/(2+x)$

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

or $14 x = 20 - 8 = 12$ $14x=20-8=12$ and hence $x = \frac{12}{14} = \frac{6}{7}$ $x=12/14=6/7$ and $t = \frac{4}{2 - \frac{6}{7}} = \frac{4}{\frac{8}{7}} = 4 \times \frac{7}{8} = \frac{7}{2}$ $t=4/(2-6/7)=4/(8/7)=4xx7/8=7/2$ hours.

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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?

1 Answer

Explanation:

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