SOLUTION: A fisherman rows 12 miles downstream in the same amount of time he rows 4miles upstream, if the current is 6 miles per hour. Find how long it takes for him to cover 12 miles witho

Question 1124828: A fisherman rows 12 miles downstream in the same amount of time he rows 4miles upstream, if the current is 6 miles per hour. Find how long it takes for him to cover 12 miles without any current.
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance.
fisherman rows 12 miles downstream in the same amount of time that he rows 4 miles upstream.
let T equal the time.
the formula going downstream is R * T = 12
the formula going upstream is R * T = 4
the current itself is 6 miles per hour.
going downstream the current is additive and going upstream the current is subtractive.
the rate going down stream becomes (R + 6) * T = 12
the rate going up stream becomes (R - 6) * T = 4.
simplify these two equations to get:
RT + 6T = 12
RT - 6T = 4
subtract the second equation from the first to get:
12T = 8
solve for T to get T = 8/12 = 2/3 of an hour.
going downstream, the equation becomes (R+6) * 2/3 = 12.
simplify to get 2/3 * R + 2/3 * 6 = 12.
solve for R to get R = (12 - 2/3 * 6) / (2/3) = 12.
the speed of the boat without any current is 12 miles per hour.
going downstream, the formula becomes (12 + 6) * 2/3 = 12 which becomes 18 * 2/3 = 12 which becomes 12 = 12.
going upstream, the formula becomes (12 - 6) * 2/3 = 4 which becomes 6 * 2/3 = 4 which becomes 4 = 4.
both equations are true when R = 12, therefore the solution looks good.
the speed of the boat in still water is 12 miles per hour.
in still water, the formula of R * T = 12 becomes 12 * T = 12 which results in T = 1.
in still water, it would take him 1 hour to go 12 miles.
that's your solution.

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE downstream r+6 12/(r+6) 12 upstream r-6 4/(r-6) 4

-

----------speed if no current

This 12 mile distance, if done without a current, would take 1 hour.
RELATED QUESTIONS
A fisherman on the river rows 9 miles downstream in the same amount of time he rows 3... (answered by nerdybill)
Michael rows 8 mph in still water. If he rows 24 miles downstream in the same amount of... (answered by solver91311)
when angelo burnini rows his gondola in still water(with no current) in venice,italy, he... (answered by ptaylor)
Junior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream (answered by Nate,mathdude2)
Juniors boat will go 15 miles per hour in still water. If he can go 12 miles downstream... (answered by Grinnell)
Junior's boat will go 15 miles per hour in still water. if he can go 12 miles downstream... (answered by solver91311)
Junior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream... (answered by nyc_function)
junior's boat will go 15 miles per hour in still water. if he can go 12 miles downstream... (answered by mananth)
Juniors boat will go 15 miles per hour in still water. If he can go 12 miles downstream... (answered by lwsshak3)