Question 1099112
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.