# A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. How do you find the speed the kayaker would make in still water?

Aug 5, 2018

$\frac{6}{5} m p h$

#### Explanation:

D = RT
As the Distance is the same

${R}_{1} \times {T}_{1} = {R}_{2} \times {T}_{2}$

Let K equal the rate of the Kayaker in still water

$\left(6 + K\right) \times 2 = \left(6 - K\right) \times 3$

Multiplying across the parenthesis gives

$12 + 2 K = 18 - 3 K$

Adding the opposite to both sides of the equation gives

$12 - 12 + 2 K + 3 K = 18 - 12 - 3 K + 3 K$

The result is

$5 K = 6$

Dividing both sides by 5

$5 \frac{K}{5} = \frac{6}{5}$

$K = \frac{6}{5}$