SOLUTION: A boat can travel 5 mile upstream and 5 miles downstream in a total of 6 hours. If the speed of the current is 2 mph, what is the speed of the boat in still water?

Hi

speed of the current is 2 mph

Let (x+2mph) and (x-2mph) represent the speed of the boat down and upstream respectively,

D = r*t  OR t = D/r

Question states*** (total time up and down is 6 hr)

 5/(x+2) + 5/(x-2) = 6  |multiplying thru by (x+2)(x-2)

5(x+2) + 5(x-2)=6(x+2)(x-2)

 10x = 6(x^2 - 4)

   6x^2 -10x - 24 = 0

  2(3x^2 -5x - 12) = 0

   (3x^2 -5x - 12)= 0

factoring

   (3x +4)(x-3)= 0 Note:SUM of the inner product(4x) and the outer product(-9x) = -5x

   (3x +4)= 0 |tossing out negative solution for speed

     (x-3)= 0  x = 3mph, speed of boat in still water



CHECKING our Answer***

   5/5 + 5/1 = 6hr