SOLUTION: A river flows at 3mph. A boat takes 1 hour longer to sail 36 miles upstream than to return. What is the speed of the boat in still water? I have worked for hours on this prob

Question 190300: A river flows at 3mph. A boat takes 1 hour longer to sail 36 miles upstream than to return. What is the speed of the boat in still water?
I have worked for hours on this problem and get equations that seem almost right but do not give me the answer. My math major friend cannot figure it out either. I'd appreciate if you would help me please. Thank you.
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=rate or speed of boat in still water
Upstream, we subtract speed of current; downstream we add
Time to travel downstream=36/(r+3)
Time to travel upstream=36/(r-3)
Now we are told that the time upstream is one hour longer than the time downstream, so:
(36/(r+3))+1=36/(r-3) multiply each side by (r+3)(r-3)
36(r-3)+(r+3)(r-3)=36(r+3) get rid of parens
36r-108+r^2-9=36r+108 subtract 36r and also 108 to each side:
36r-108-108+r^2-9-36r=36r-36r+108-108 collect like terms
r^2-216-9=0
r^2-225=0 add 225 to each side
r^2=225 take square root of each side
r=+ or -15 mph negelect the negetive value for r; speeds are positive
r=15 mph------------------speed of boat in still water
CK
(36/18)+1=36/12
2+1=3
3=3
Hope this helps---ptaylor
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