Question

1. a kayaker paddles 3 km upstream in the same time that it takes to paddle 9 km downstream. the average speed of the current is 1 km/h. what is the average speed of the kayak in still water?

Explanation:

Step1: Define variable for kayak speed

Let $x$ = speed of kayak in still water (km/h).
Upstream speed: $x - 1$ km/h, downstream speed: $x + 1$ km/h.

Step2: Set time equality (time = distance/speed)

Time upstream = Time downstream:
$\frac{3}{x-1} = \frac{9}{x+1}$

Step3: Cross-multiply to solve for $x$

$3(x+1) = 9(x-1)$
$3x + 3 = 9x - 9$
$3 + 9 = 9x - 3x$
$12 = 6x$
$x = \frac{12}{6} = 2$

Answer:

2 km/h