The Gold Rivers current is 6 mph A boat travels 50 miles dow

The Gold River\'s current is 6 mph. A boat travels 50 miles downstream in the same time that it takes to travel 30 miles upstream. What is the speed of the boat in still water?

Solution

Let r=rate (speed) of the boat in still water
distance(d) = rate(r) times time(t) or d=rt; r=d/t and t=d/r
rate upstream=(r-6)
rate downstream=(r+6)
We are told that time upstream=time downstream
time upstream=30/(r-6)
time downstream=50/(r+6)
So our equation to solve is:
30/(r-6)=50/(r+6) multiply both sides by (r+6)(r-6) or cross-multiply
30(r+6)=50(r-6) get rid of parens (distributive law)
30r+180=50r-300 subtract 50r and also 180 from both sides
30r-50r+180-180=50r-50r-300-180 collect like terms
-20r=-480 divide both sides by -20
r=24 mph---------------------rate (speed) in still water
CK
30/(24-6)=50/(24+6)
30/18=50/30
5/3=5/3