SOLUTION: Swimming downstream, a swimmer can cover 0.5 mile in 6 minutes. It takes the swimmer 30 minutes to swim back up the stream. Find the speed of the swimmer in still water and the spe

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Swimming downstream, a swimmer can cover 0.5 mile in 6 minutes. It takes the swimmer 30 minutes to swim back up the stream. Find the speed of the swimmer in still water and the spe      Log On


   

Question 384440: Swimming downstream, a swimmer can cover 0.5 mile in 6 minutes. It takes the swimmer 30 minutes to swim back up the stream. Find the speed of the swimmer in still water and the speed of the current.
Found 2 solutions by ewatrrr, amalm06:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,         

Let x +c and x-c represent speeds downstream and upstream respectively

Question states:  D = r*t 6 min = 1/10hr

 1/10(x+c)= .5mi

     x = 5 - c

 1/2(x -c)=.5mi  substituting for x, to solve for c

 1/2[(5 - c) - c] = .5mi

      5 -2c  = 1

          4 = 2c

          c = 2mph, the speed of the current, speed in still water is 3mph (5-2)



CHECKING our Answer

 .1hr * 5mph = .5mi

Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
Downstream: d=rt-->(v+c)(6)=0.5-->v+c=0.08333
Upstream: d=rt-->(v-c)(30)=0.5-->v-c=0.01666
v=c+0.01666--> 0.01666+2c=0.08333-->2c=0.06667-->c=0.0333 mi/min= 2 mi/hr
v=0.05003 mi/hr=3 mi/hr
Speed of swimmer in still water: 3 mi/hr (Answer)
Speed of current: 2 mi/hr (Answer)