Question 1099109: Alvin paddled for 5 hours with a 3-km/h current to reach a campsite. The return trip against the same current took 8 hours.
What is the speed of the boat in still water?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
let r = rate and t = time and d = distance
going downstream, the formula becomes (r+3) * 5 = d
coming back upstream, the formula becomes (r-3) * 8 = d
the distance downstream is the same as the distance upstream, so (r+3) * 5 = (r-3) * 8
simplify to get 5r + 15 = 8r - 24
subtract 5r from both sides of this equation and add 24 to both sides of this equation to get 39 = 3r
solve for r to get r = 39/3 = 13
he paddles at 13 kilometers per hour.
going downstream, the stream adds 3 kilometers per hours to this to get 16 kilometers per hour for 5 hours = 80 kilometers.
coming back upstream, the stream subtracts 3 kilometers from this to get 10 kilometers per hour for 8 hours = 80 kilometers.
the distance downstream and upstream is the same at 80 kilometers.
the speed of the boat is 13 kilometers per hour
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