Question

On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 34 miles with the wind, she could go only 18 miles against the wind. What is her normal rowing speed with no wind?

Answer 1

recall your d = rt, distance = rate * time.

j = Jaime's rate

so with the wind her rate is j + 4, and without the wind her rate is j - 4, we also know that she can do with the wind 34 miles and against it 18 miles all within the same amount of time of t hours.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{with the wind}&34&j+4&t\\ \textit{against the wind}&18&j-4&t \end{array} \\\\\\ \begin{cases} 34=(j+4)t\implies \frac{34}{j+4}=\boxed{t}\\\\ 18=(j-4)t\\ -------------\\ 18=(j-4)\left( \boxed{\frac{34}{j+4}} \right) \end{cases} \\\\\\ 18(j+4)=(j-4)34\implies 18j+72=34j-136 \\\\\\ 208=16j\implies \cfrac{208}{16}=j\implies 13=j$