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Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?

Answer is supposed to be 3600 meters. But how do I approach the problem ?

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    Start with a sketch then model the position functions. Translate the information from the text into proper equations. Solve. – 2017-02-17
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    https://www.theproblemsite.com/problems/high-school-math/2004/row-row-row http://www.beatthegmat.com/boat-and-stream-t277140.html – 2017-02-17
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    how about the river has a width w, the boats have speeds s1 and s2 - come up with equations for how far they have travelled when they meet – 2017-02-17

2 Answers 2

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Hint:

Let $x$ be the width of the river. It is given that, when they have met the first time, boat$_1$ has travelled $1400$ m and boat$_2$, $(1400-x)$ metres.

When they meet for the second time, boat$_1$ has travelled $600+(x-1400) = (x-800)$ m, and boat$_2$, $1400 +(x-600) = (x+800)$ m.

Note that, the relationship of the distances each traveled, is the same to both meetings. Thus, $$\frac{1400}{1400-x} = \frac{x-800}{x+800}$$ $$\Rightarrow x= ?$$ Hope you can take it from here.

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    The solutions to the equation you provide are not in $\mathbb{R}$. I think it is because boat$_{1}$ did not travel $1400-x$ to the first meeting, it traveled $x-1400$. Similarly, to the second meeting the boats have traveled $x+600$ and $2x-600$ respectively. Using $1400$, $x-1400$, $x+600$ and $2x-600$ provides correct answer. – 2017-02-17
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Hint: Let $m_1$ be the speed, in meters per second, of the fist boat and similarly for $m_2$. Let $s_{1}$ be the time, in seconds when they meet for the first time and $s_{2}$ be the time when they meet for the second time. Let $w$ be the width of the river. From your text, $s_1m_1+s_1m_2=w$ and $s_2m_1+s_2m_2=3w$. Assuming 'one bank' is the one from which boat $1$ started, you also know $s_1m_1=1400$ and $s_2m_1=w+600$. You can do the rest.