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There are two docks, dock A and Dock B, on a large lake. The distance between the two docks is 72.5 km. Dock B is directly east of dock A. One day, a steam boat leaves from dock A at noon, and heads eastward. At the same time, a large ferry leaves from dock B, and heads southward. The steam boat travels with a speed of 20 km/hr. The speed of the ferry is 8 km/hr.

The visibility on the lake is 20 miles that day. Would passengers on one boat ever have a chance to see the other boat? If yes, how long is their “window of opportunity”?

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    Did you try something?2012-10-31
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    You mean 20 km right?2012-10-31

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Hint: Let the origin be at $B$. If $t$ is the time since noon in hours, the steam boat position is $(-72.5+20t,0)$. The ferry position is $(0,-8t)$. Note the different units on visibility.

Added: The distance between them at time $t$ is then $\sqrt{(-72.5+20t)^2+(8t)^2}$

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    @NGPP1: I have added another step.2012-11-01
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    @NGPP1: it seems unlikely as the steam boat arrives in less than 4 hours. What is $D$? It hasn't been in the problem before. The largest distance around is 72.5 km, as well.2012-11-01
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    @NGPP1: the distance is in km, and should be 20*1.609, the range of visibility. I don't know where $6$ came from. You are solving for the time that gives that distance.2012-11-01
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    @NGPP1: I got 1.609 as the conversion between miles and km. You are given the distance as 20 miles. So $D^2=(20*1.609)^2=(-72.5+20t)^2+(8t)^2$. Expand and you have a quadratic in $t$2012-11-01
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    @NGPP1: yes. But the answer I get needs some thought at the end. The equation as written presumes the steam boat continues past the dock, probably not real (but the problem doesn't say anything to the contrary).2012-11-01
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    @NGPP1: you lost the left hand side. The constant term is about 4220.7, which yields positive solutions.2012-11-01