SOLUTION: 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?

Click here to see ALL problems on Travel Word Problems

Question 110487: 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?
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
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
Hope this helps---ptaylor