The current in a typical mississippi river shipping route flows at a rate of 4mph. In order for a barge to travel 24mi upriver and then return in a total of 5hr, aproximately how fast must the barge be able to travel in still water?

speed of boat in still water ---> x mph

speed upriver = x-4 mph
time upriver = 24/(x-4)

speed downriver = x+4 mph
time downriver = 24/(x+4)

24/(x-4) + 24/(x+4) = 5
times (x-4)(x+4)
24(x+4) + 24(x-4) = 5(x+4)(x-4)
24x + 96 + 24x - 96 = 5x^2 -80
5x^2 - 48x -80 = 0
x = (48 ± √3904)/10 = 11.048 or a negative

so the boat's speed would be appr. 11 mph

check:
24/7 + 25/15 = appr. 5.03 , looks good