Question

The picture is the question im struggling with! Im not sure how to do the work

Answer 1

`\text{ Equation: }(10)/(7-c)=(25)/(7+c)`

3 miles per hour

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:

`\begin{gathered} \text{ Time to travel 10 miles upstream =}(10)/(\:7-c) \\ \\ \text{ Time to travel 25 miles downstream}=(25)/(7+c) \end{gathered}`

The time is equal, then, the equation would be:

`(10)/(\:7-c)=(25)/(\:7+c)`

We solve for c, just like this:

`\begin{gathered} 10\left(7+c\right)=25\left(7-c\right) \\ \\ 70+10c=175-25c \\ \\ 25c+10c=175-70 \\ \\ 35c=105 \\ \\ c=(105)/(35) \\ \\ c=\text{ 3 miles per hour } \end{gathered}`

The speed of the river is 3 miles per hour.