Questiona boat going with the current travels 110 miles over 5 hours. When it was traveling back against the current it took II hours. rate of boat in still water $\qquad$ rate of current. $\qquad$

Studdy Solution
Solve the system of equations to find the rates.
First, simplify both equations:
Equation 1: $5b + 5c = 110$ Equation 2: $11b - 11c = 110$
Divide Equation 1 by 5:
$$b + c = 22$$
Divide Equation 2 by 11:
$$b - c = 10$$
Add the two equations to eliminate $c$:
$$(b + c) + (b - c) = 22 + 10$$ $$2b = 32$$ $$b = 16$$
Substitute $b = 16$ back into the equation $b + c = 22$:
$$16 + c = 22$$ $$c = 6$$
The rate of the boat in still water is $\boxed{16}$ miles per hour, and the rate of the current is $\boxed{6}$ miles per hour.