Question

ina crespo rowed 9 miles down the habashabee river in 1.5 hours, but the return trip took her 3 hours. find the rate ina rows in still water and the rate of the current. let x represent the rate ina can row in still water and let y represent the rate of the current.
downstream
upstream
the current flows □ mph.
ina can row □ mph in still water.

Explanation:

Step1: Set up downstream - rate equation

The distance formula is $d = r\times t$. For the downstream trip, $d = 9$ miles, $t = 1.5$ hours, and the rate $r=x + y$. So, $9=(x + y)\times1.5$. Divide both sides by 1.5: $x + y=\frac{9}{1.5}=6$.

Step2: Set up upstream - rate equation

For the upstream trip, $d = 9$ miles, $t = 3$ hours, and the rate $r=x - y$. So, $9=(x - y)\times3$. Divide both sides by 3: $x - y = 3$.

Step3: Solve the system of equations

We have the system of equations

$$\begin{cases}x + y=6\\x - y=3\end{cases}$$

. Add the two equations together: $(x + y)+(x - y)=6 + 3$. This simplifies to $2x=9$, so $x = 4.5$.

Step4: Find the value of y

Substitute $x = 4.5$ into the first - equation $x + y=6$. Then $4.5+y=6$. Subtract 4.5 from both sides: $y=6 - 4.5 = 1.5$.

Answer:

Ina can row 4.5 mph in still water and the current flows 1.5 mph.