Question 1007823: This word problem is a doozy. Anyone got any ideas?
A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 36 hours. What is the speed of the boat in still water? What is the speed of the current?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! No worries. Remember that rate times time equals distance, or rt=d.
Let us call the rate in still water, r.
Let us call the rate of the current, c.
Then, from the facts in the problem we have
(r+c)(12) = 252 and
(r-c)(36) = 252
We can multiply these out and get
12r + 12c = 252 and
36r - 36c = 252
Now multiply the top one by three and add it to the second one...we get
36r - 36c = 252
+(36r + 36c = 756)
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72r = 1008
Now divide by 72 and get
r = 14 miles per hour
c can be found by substituting into the very first equation...
(14+c)(12)=252
Divide by 12 and get
14 + c = 21
c = 7 mph
Ta-daa!
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