SOLUTION: Hi, I need some help with working out this motion problem, thanks! "Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Hi, I need some help with working out this motion problem, thanks! "Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same      Log On


   

Question 1120738: Hi, I need some help with working out this motion problem, thanks!
"Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find the rate of the current and the rate that Gertrude was rowing downstream."
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
                SPEED        TIME    DISTANCE

downstream        r+c          4       24

upstream         2r-c          4       24

system%284%28r%2Bc%29=24%2C4%282r-c%29=24%29
-
system%28r%2Bc=6%2C2r-c=6%29

3r=12

highlight%28r=4%29-------boat, downstream speed
-
highlight%28c=2%29-------current

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = the speed of the boat going downstream
+2s+ = the speed going upstream
Let +c+ = the speed of the current
——————————————————-
Equation for going downstream
(1) +24+=+%28+s+%2B+c+%29%2A4+
Equation for going upstream
(2) +24+=+%28+2s+-+c+%29%2A4+
——————————————-
(1) +s+%2B+c+=+6+
(2) +2s+-+c+=+6+
———————————-
Add the equations
+3s+=+12+
+s+=+4+
And
(1) +4+%2B+c+=+6+
(1) +c+=+2+
———————————-
The rate of the current was 2 mi/hr
She was rowing at a rate of 4 mi/hr going downstream