The average speed of the boat in still water is calculated to be √74 mi/hr, which is approximately 8.6 mi/hr by setting up an equation using the concept of relative speed in river current problems.
To determine the average speed of a boat in still water, we can use the concept of relative speed in river current problems.
Let the speed of the boat in still water be v miles per hour, and the speed of the current is given as 2 mi/hr.
When the boat is going downstream, the effective speed is v + 2 mi/hr. On the return trip upstream, against the current, the effective speed is v - 2 mi/hr.
We know that it takes 8 hours longer to travel upstream than downstream over the same distance of 280 miles.
Using the formula time = distance/speed, the downstream time is 280 / (v + 2) hours, and the upstream time is 280 / (v - 2) hours.
Setting up the equation based on the extra 8 hours needed for the upstream trip, we have:
280 / (v - 2) - 280 / (v + 2) = 8
Solving for v:
280(v + 2) - 280(v - 2) = 8(v^2 - 4)
560 = 8v^2 - 32
v^2 = 74
v = √74
The average speed of the boat in still water is √74 mi/hr, which is approximately 8.6 mi/hr.