Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.
<h3>What is the
relation between velocity, distance and time?</h3>
Velocity is distance divided by time, hence:
v = d/t
A small motorboat travels 12mph in still water. With the current, upstream, 46 miles are traveled in t hours, hence:
12 + r = 46/t
r = 46/t - 12
Downstream, the time is of t + 2 hours, hence:
12 - r = 46/(t + 2)
r = 12 - 46/(t + 2)
Hence, equaling the values for r:
46/t - 12 = 12 - 46/(t + 2)
46/t + 46/(t + 2) = 24
![\frac{46t + 92 + 46t}{t(t + 2)} = 24](https://tex.z-dn.net/?f=%5Cfrac%7B46t%20%2B%2092%20%2B%2046t%7D%7Bt%28t%20%2B%202%29%7D%20%3D%2024)
92t + 92 = 24t² + 48t
24t² - 44t - 92 = 0
Using a quadratic equation calculator, the solution is t = 3. Hence the rate is found as follows:
r = 46/t - 12 = 46/3 - 12 = 3.33 mph.
More can be learned about the relation between velocity, distance and time at brainly.com/question/28155966
#SPJ1