Question

A small motorboat travels 12mph in still water. It takes 2 hours longer to travel 46 miles going upstream than it does going downstream. Find the rate of the current

Answer 1

Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.

What is the relation between velocity, distance and time?

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

$\frac{46t + 92 + 46t}{t(t + 2)} = 24$

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

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