Question

A small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 8+x= rate going downstream and 8−x= rate going upstream.)(Round your answer to the nearest tenth.)

Answer 1

The rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.

What is a quadratic equation?

Any equation of the form $\rm ax^2+bx+c=0$  Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

Let's suppose the rate of the current  = r

The time it takes to go downstream + 4 hours   = time to go upstream

As we know the:

$\rm Time = \dfrac{Distance}{ Rate }$

Now,

$\rm \dfrac{44}{ (8 + r)} + 3 = \dfrac{44}{ (8 - r)}$

After solving:

$\rm \dfrac{44}{ (8 - r)}-\dfrac{44}{ (8 + r)} =3$

After cross multiplication

44(8+r) - 44(8-r) = 3(8+r)(8-r)

88r = 3(64 - r²)

3r² + 88r - 192 = 0

After solving the above quadratic equation, we get:

r = 2.03 or

r=−31.37 (reject as it is negative)

So, the r  =2.03 mph

Thus, the rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.

Learn more about quadratic equations here:

brainly.com/question/2263981

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