Your boat will go 15 miles per hour in still water If you ca

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?

Solution

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