58. Time to Cross a River in Still Water A paddler takes 4 hours to cross a river when rowing against the current and 3 hours to cross the same distance when rowing with the current.Assuming he exerts the same effort each time, how long would the crossing take if the water were perfectly still? Added 31 July 2012 Show Hint Show Solution Hint: Let b be the paddler’s speed in still water and c the speed of the current. Write two equations for the distance using the times given, then solve for b. Solution: Let the width of the river be d.Against the current: \(\dfrac{d}{4}=b-c\).With the current: \(\dfrac{d}{3}=b+c\).Add the two equations:\(\dfrac{d}{4}+\dfrac{d}{3}=2b \;\Rightarrow\; \dfrac{7d}{12}=2b \;\Rightarrow\; b=\dfrac{7d}{24}.\)The time required in still water is\(\displaystyle \text{time}=\frac{d}{b}=\frac{d}{\tfrac{7d}{24}}=\frac{24}{7}\text{ hours}\approx3\text{ h }25\text{ min}.\)
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