SOLUTION: anna rows a boat downstream for 216 miles the return trip upstream took 18 hours longer. if the current flows at 3mph, how fast does anna row in still water?

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Question 635210: anna rows a boat downstream for 216 miles the return trip upstream took 18 hours longer. if the current flows at 3mph, how fast does anna row in still water?
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=Anna's rowing speed in still water
Then r+3=Anna's rowing speed downstream
and
r-3=Anna's rowing speed upstream
Time required to row downstream=216/(r+3)
Time required to row upstream=216/(r-3) and we are told that this took 18 hours longer, sooooooo:
216/(r+3) +18=216/(r-3) multiply each term by (r+3)(r-3)
216(r-3)+18(r+3)(r-3)=216(r+3) next divide each term by 18 and simplify
12r-36+r^2-9=12r+36 collect like terms
r^2-81=0
r=+or-9 ---- -9 is no good; can't have negative rowing speeds
so
r= 9 mph Anna's roving speed in still water
CK
216/12 + 18=216/6
18+18=36
36=36
Hope this helps---ptaylor