Final answer:
To determine Brigeth's rowing speed in still water, we set up and solve a system of equations based on the distances and times of the upstream and downstream trips. Considering the river current speed, we use the equations 168 = (B + 4) T for downstream and 168 = (B - 4) (T + 16) for upstream to find Brigeth's speed (B) and the time taken downstream (T).
Step-by-step explanation:
The question asks to determine the speed at which Brigeth rows the boat in still water. Given that the current flows at 4 mph, we can use this information along with the distances and times provided to calculate Brigeth's rowing speed in still water through a system of equations. To solve this problem, we set up two equations representing the upstream and downstream trips.
Let's define B as Brigeth's rowing speed in still water in mph. When rowing downstream, the speed of the boat is B + 4 mph, and when rowing upstream, the speed is B - 4 mph. We are told that the downstream distance is 168 miles and the upstream journey took 16 hours longer.
For the downstream trip: Distance = Speed × Time which translates to 168 = (B + 4) T where T is the time taken downstream.
For the upstream trip: Distance = Speed × Time which translates to 168 = (B - 4) (T + 16).
We now have two equations:
168 = (B + 4) T
168 = (B - 4) (T + 16)
By solving these equations simultaneously, we can find the values of B (Brigeth's rowing speed) and T (time taken for the downstream trip).