Question

Question 55 ptsIris likes to go for boat rides along the river with her family. In still water, the boat travels 6kilometers per hour. In the river, it takes them the same amount of time to go upstream 5 kilometersas it does to go downstream 10 kilometers. Write and solve an equation to calculate the speed ofthe river, r. Explain or show your reasoning

Answer 1

Let's define

r: speed of the river

By definition:

speed = distance/time

The speed of the boat depends on the boat's own speed and the speed of the river. Then upstream:

6 - r= 5/t

or

t = 5/(6 - r)

and downstream:

6 + r= 10/t

or

t = 10/(6 + r)

It takes them the same amount of time to go upstream as it does to go downstream, then:

$\begin{gathered} \frac{5}{6-r}=\frac{10}{6+r} \\ 5\cdot(6+r)=10\cdot(6-r) \\ 30+5r=60-10r \\ 5r+10r=60-30 \\ 15r=30 \\ r=\frac{30}{15} \\ r=2 \end{gathered}$

The speed of the river is 2 kilometers per hour