Discussion
A woman takes 1/11 time in rowing a certain distance downstream than upstream. What is the ratio of the speed of the current to the speed of the boat in still water?
Answer: D
The ratio of the speed of the current to the speed of the boat is 5/6.
Read as the key does, the downstream trip takes 1/11 of the upstream time over the same distance, so the speeds are in the inverse ratio. Let b be the speed in still water and c the current.
\[ \begin{aligned} \frac{b - c}{b + c} &= \frac{1}{11} \\ 11b - 11c &= b + c \\ 10b &= 12c \Rightarrow \frac{c}{b} = \frac{5}{6} \end{aligned} \]
6/5 is the same ratio upside down (boat to current). 11/5 and 11/6 come from mixing the 11 into the answer instead of solving for it.
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