Edit View History Bookmarks Profiles Tob Window Help texs classroom Link ALEKS - Sydney Cano - Know Edgenifity Cowboy Channelt Google Docs Dashboard Google Dive e2020.geniusals. Course Map - Iman. Wrzant Knownedge Check Question 3 Sydney A rowing team rowed 60 miles while going with the current in the same amount of time as it took to row 10 miles going against the current. The rate of the Expatiat current was 5 miles per hour. Find the rate of the rowing team in still water. Rate of the team in still water: \( \square \) miles/hour

Let's denote the rate of the rowing team in still water as \( r \) miles per hour. Given that the rowing team rowed 60 miles with the current in the same amount of time as it took to row 10 miles against the current, we can set up the following equation based on the formula for distance, speed, and time: \[ \frac{60}{r + 5} = \frac{10}{r - 5} \] Now, we can solve this equation to find the rate of the rowing team in still water. Solve the equation by following steps: - step0: Solve for \(r\): \(\frac{60}{r+5}=\frac{10}{r-5}\) - step1: Find the domain: \(\frac{60}{r+5}=\frac{10}{r-5},r \in \left(-\infty,-5\right)\cup \left(-5,5\right)\cup \left(5,+\infty\right)\) - step2: Cross multiply: \(60\left(r-5\right)=\left(r+5\right)\times 10\) - step3: Simplify the equation: \(60\left(r-5\right)=10\left(r+5\right)\) - step4: Rewrite the expression: \(10\times 6\left(r-5\right)=10\left(r+5\right)\) - step5: Evaluate: \(6\left(r-5\right)=r+5\) - step6: Expand the expression: \(6r-30=r+5\) - step7: Move the expression to the left side: \(6r-r=5+30\) - step8: Add and subtract: \(5r=5+30\) - step9: Add and subtract: \(5r=35\) - step10: Divide both sides: \(\frac{5r}{5}=\frac{35}{5}\) - step11: Divide the numbers: \(r=7\) - step12: Check if the solution is in the defined range: \(r=7,r \in \left(-\infty,-5\right)\cup \left(-5,5\right)\cup \left(5,+\infty\right)\) - step13: Find the intersection: \(r=7\) The rate of the rowing team in still water is 7 miles per hour.