Question

Ari can drive his boat 18 miles with the current in the same amount of time it takes to drive 10 miles against the current. If the speed of the boat is 7 knots, solve the equation$\frac{18}{7+c}=\frac{10}{7-c}$ for c to find the speed of the current.

Short answer

The speed of the current is$c=2.$

Step-by-step solution

Step 1. Given Information.

The given equation is$\frac{18}{7+c}=\frac{10}{7-c}.$

Step 2. Solve

To solve the equation and find the speed of the current, cross multiply the given equation

$$\begin{gathered} \frac{18}{7+c}=\frac{10}{7-c} \\ 18\left(7-c\right)=10\left(7+c\right) \\ 126-18c=70+10c \\ 126-70=10c+18c \\ 56=28c \end{gathered}$$

To isolate cdivide $28$on both sides

$$\begin{gathered} \frac{56}{28}=\frac{28c}{28} \\ 2=c \end{gathered}$$