Final answer:
The speed of the boat in still water is 11 mph, which is calculated by setting the total time for the upstream and downstream trip, with respective speeds adjusted by the current, to be equal to 13 hours and solving the resulting equation.
Step-by-step explanation:
The question asks for the speed of the boat in still water when it travels 19 miles upstream and 19 miles downstream in a total of 13 hours, with a stream speed of 4 mph.
Let's denote the speed of the boat in still water as v mph. When traveling upstream, the effective speed of the boat is v - 4 mph, and when traveling downstream, the effective speed is
v + 4 mph.
Using the formula
time = distance / speed,
we can set up two equations to represent the total time spent traveling in each direction:
- Time upstream: (19 / (v - 4)) hours
- Time downstream: (19 / (v + 4)) hours
The total time for both parts of the trip is 13 hours, so the equation is:
(19 / (v - 4)) + (19 / (v + 4)) = 13
Solving this equation, we find that the boat's speed in still water v is 11 mph.