ANSWER:
[tex]\text{ Equation: }\frac{10}{7-c}=\frac{25}{7+c}[/tex]
3 miles per hour
STEP-BY-STEP EXPLANATION:
Let the speed of the river current is c miles/hour
Going downstream, the speed of the kayak is (7-c) miles/hour
Going upstream, the speed of the kayak is (7+c) miles/hour
Therefore:
[tex]\begin{gathered} \text{ Time to travel 10 miles upstream =}\frac{10}{\:7-c} \\ \\ \text{ Time to travel 25 miles downstream}=\frac{25}{7+c} \end{gathered}[/tex]
The time is equal, then, the equation would be:
[tex]\frac{10}{\:7-c}=\frac{25}{\:7+c}[/tex]
We solve for c, just like this:
[tex]\begin{gathered} 10\left(7+c\right)=25\left(7-c\right) \\ \\ 70+10c=175-25c \\ \\ 25c+10c=175-70 \\ \\ 35c=105 \\ \\ c=\frac{105}{35} \\ \\ c=\text{ 3 miles per hour } \end{gathered}[/tex]
The speed of the river is 3 miles per hour.
