Question

Susie enjoys spending her afternoons kayaking. One afternoon she was kayaking on a river 3 miles upstream, and 3 miles downstream in a total of 4 hours. In still water, Susie can Kayak at an average speed of 2 miles per hour. Based on this information, what a reasonable estimation of the current measured in miles per hour.

Answer 1

Using the relation between velocity, distance and time, it is found that a reasonable estimation of the current is of 1 mph.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, hence:

$v = \frac{d}{t}$

Upstream, against the current, he traveled 3 miles in t hours, hence the equation is:

$2 - c = \frac{3}{t}$

$c = 2 - \frac{3}{t}$

Downstream, with the current, he traveled 3 miles in 4 - t hours, hence the equation is:

$2 + c = \frac{3}{4 - t}$

Hence:

$c = \frac{3}{4 - t} - 2$

Then, taking the two equal equations:

$2 - \frac{3}{t} = \frac{3}{4 - t} - 2$

$\frac{3}{4 - t} + \frac{3}{t} = 4$

$\frac{3t + 12 - 3t}{t(4 - t)} = 4$

12 = -4t² + 16t

4t² - 16t + 12 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0.

The current is positive, hence:

$c = 2 - \frac{3}{3}$

c = 2 - 1

c = 1 mph.

More can be learned about the relation between velocity, distance and time at brainly.com/question/24316569

#SPJ1