SOLUTION: Your boat will go 15 miles per hour in still water. If you can go 12 miles downstream in the same amount of time it takes to go 9 miles upstream, then what is the speed of the cur

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Question 152435: Your boat will go 15 miles per hour in still water. If you can go 12 miles downstream in the same amount of time it takes to go 9 miles upstream, then what is the speed of the current?
Answer by ptaylor(2198) About Me  (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(speed) of the current
(We know that speed upstream=15-r and speed downstream=15+r)
Time to go upstream=9/(15-r)
Time to go downstream=12/(15+r)
Now we are told that the above two times are equal, so our equation to solve is:
9/(15-r)=12/(15+r) multiply each side by (15-r)(15+r) or cross multiply
9(15+r)=12(15-r) get rid of paren
135+9r=180-12r subtract 135 from and add 12r to each side
135-135+9r+12r=180-135-12r+12r collect like terms
21r=45 divide each side by 21
r=2 1/7 mph---------------------speed of current
CK
9/(15-2 1/7)=12/(15+2 1/7) or
9/(12 6/7)=12/(17 1/7) and this equals
9/(90/7)=12/(120/7) or
63/90=84/120 and
7/10=7/10
Hope this helps----ptaylor