Aboat traveled downstream a distance of 80 mi and then came right back. if the speed of the current was 7 mph and the total trip took 3 hours and 20 minutes, find the average speed of the boat relative to the water.

Recall your d = rt, distance = rate * time.

going forth and back is 80 miles, thus upstream as well as downstream is just 80 miles.

now, bear in mind that say, the boat has a "still water" of "b", when going downstream, is not going "b" fast is going "b+7" because the current's is adding to it, likewise when is going upstream is going "b-7" because is going against the current and thus the current is eroding speed from it.

now, the whole trip took 3 hours and 20 minutes, bearing in mind that 20 minutes is 1/3 of an hour, so is 3 and 1/3 hours, or 10/3 of hours.

if say it took "t" hours going down, then going up it took the slack from 10/3 and "t", that is, it took "10/3 - t".