Fat Chance can row his boat 9 miles up Moss Creek in the sam

Fat Chance can row his boat 9 miles up Moss Creek in the same time that it takes him to row 15 miles down the creek. If fat can row 2 miles per hour in still water, how fast is the current in Moss Creek?

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 in Moss Creek
Fat\'s rate upstream is (2-r) and his rate downstream is (2+r)
Fat\'s time upstream is (d/r)=9/(2-r)
Fat\'s time downstream is (d/r)=15/(2+r)
Now we are told that the above times are equal, so:
9/(2-r)=15/(2+r) multiply each side by (2-r)(2+r) or cross-multiply
9(2+r)=15(2-r) get rid of parens
18+9r=30-15r subtract 9r and also 30 from each side
18-30+9r-9r=-15r-9r+30-30 collect like terms
-12=-24r divide both sides by -24
r=0.5 mph-----------------------------rate of current
CK
9/1.5=15/2.5
6=6