Question 1099112: On a weekend outing, Carlos rents a motorboat for 10 hours to travel down the river and back. The rental operator tells him to go for 4 hours downstream, leaving 6 hours to return upstream.
If the river current flows at a speed of 5 mph, how fast must Carlos travel in order to return in 10 hours?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
let r = rate
time is in hours
distance is in miles
going downstream, the formula becomes (r+5)*4 = distance downstream
going upstream, the formula becomes (r-5) * 6 = distance upstream
the distance downstream is the same as the distance upstream.
therefore (r+5)*4 = (r-5)*6
simplify to get 4r+20 = 6r-30
subtract 4r from both sides of this equation and add 30 to both sides of this equation to get 50 = 2r
solve for r to get r = 25.
his boat needs to travel at 25 miles per hour.
going downstream, the stream adds 5 miles per hour to that for a total of 30 miles per hour for 4 hours to equal a distance of 120 miles.
coming back upstream, the stream subtracts 5 miles per hour from that for a total of 20 miles per hour for 6 hours to equal a total distance of 120 miles.
carlos needs to travel 25 miles per hour to go downstream and come back upstream in 10 hours.
that's what i get.
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