SOLUTION: Please help me so this word problem. {{{ The current of a river is 4 miles per hour . A boat travels to a point 6 miles upstream and back in 2 hours. What i

Algebra ->  Equations -> SOLUTION: Please help me so this word problem. {{{ The current of a river is 4 miles per hour . A boat travels to a point 6 miles upstream and back in 2 hours. What i      Log On


   

Question 1195643: Please help me so this word problem.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note: Don't put your whole question inside the "{}" symbols; those symbols are supposed to contain only mathematical equations or expressions.

Let x be the speed of the boat in still water. Then x+4 is its speed downstream (with the current) and x-4 is its speed upstream (against the current).

Time to go upstream 6 miles: 6/(x-4)
Time to got downstream 6 miles: 6/(x+4)
The total time is 2 hours:

6%2F%28x-4%29%2B6%2F%28x%2B4%29=2

Multiply by the least common denominator, (x-4)(x+4):

6%28x%2B4%29%2B6%28x-4%29=2%28x%5E2-16%29
12x=2x%5E2-32
2x%5E2-12x-32=0
x%5E2-6x-16=0
%28x-8%29%28x%2B2%29=0
x=8 or x=-2

Obviously the negative solution makes no sense, so x=8.

ANSWER: the speed of the boat in still water is 8mph.

CHECK: 6%2F%28x-4%29%2B6%2F%28x%2B4%29=6%2F4%2B6%2F12=3%2F2%2B1%2F2=2