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
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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.
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