Final answer:
To find the speed of the current, set up equations for the boat's speed with and against the current. Solve the equation to find the speed of the current to the nearest tenths place.
Step-by-step explanation:
To find the speed of the current, we need to set up equations for the boat's speed with and against the current.
Let's assume the speed of the current is 'x' mph.
So, the boat's speed upstream (against the current) will be the boat's speed in still water minus the speed of the current: 34 - x.
Similarly, the boat's speed downstream (with the current) will be the boat's speed in still water plus the speed of the current: 34 + x.
Given that the boat goes 1075 miles upstream and 1075 miles back in a total of 68 hours, we can set up the following equation: 1075/(34 - x) + 1075/(34 + x) = 68
Simplifying and solving this equation will give us the speed of the current.
Multiply both sides of the equation by (34 - x)(34 + x) to get rid of the denominators.
Bring all the terms to one side of the equation.
Use the quadratic formula to solve for 'x' (the speed of the current).
After solving the equation, you'll find the speed of the current to the nearest tenths place.