SOLUTION: Vanessa rows a boat downstream for 42 miles. The return trip upstream took 8 hours longer. If the current flows at 2 mph, how fast does Vanessa row in still water?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Vanessa rows a boat downstream for 42 miles. The return trip upstream took 8 hours longer. If the current flows at 2 mph, how fast does Vanessa row in still water?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1185975: Vanessa rows a boat downstream for 42 miles. The return trip upstream took 8 hours longer. If the current flows at 2 mph, how fast does Vanessa row in still water?
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.
Vanessa rows a boat downstream for 42 miles. The return trip upstream took 8 hours longer.
If the current flows at 2 mph, how fast does Vanessa row in still water?
~~~~~~~~~~~ 

Let x be the rate of the boat in still water.


Then  the effective rate rowing downstream is (x+2) mph,

while the effective rate rowing upstream   is (x-2) mph.


Time rowing 42 miles downstream is  42%2F%28x%2B2%29  hours;

Time rowing 42 miles upstream   is  42%2F%28x-2%29  hours.


Time equation, according to the problem, is


    42%2F%28x-2%29 - 42%2F%28x%2B2%29 = 8   hours.


To solve this equation, multiply both sides by  (x-2)*(x+2)  and simplfy.


    42(x+2) - 42(x-2) = 8*(x-2)*(x+2)

    42x + 84 - 42x + 84 = 8*(x^2-4)

           168          = 8(x^2-4)

           21           =   x^2 - 4

           21 + 4       = x^2

           x^2          = 25

            x           = sqrt%2825%29 = 5.


ANSWER.  The boat's rate in still water is 5 miles per hour.

Solved.