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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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    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: you lost the left hand side. The constant term is about 4220.7, which yields positive solutions.2012-11-01