find speed of boat in still water and speed of current

Question

A boat traveled 336 miles downstream and back.  The trip downstream took 12 hours.  The trip back took 14 hours.  What is the speed of the boat in still water?  What is the speed of the current?

Answer 1

168 = (r-s)*14

 

168 = (r+s)*12

 

14(r - s) = 12(r+s)

14r - 14s = 12r + 12s

 

14r - 14s - 12r - 12s = 0

 

2r - 26s = 0

2r = 26s

r = 13s

 

168 = (13s-s)14

 

168 = 12s*14

 

168 = 168s

 

s=1

 

r=13(1) = 13

 

 

CHECK:

  Upstream:  (13-1)*14 = 12*14 = 168

   DOwnstream (13+1)*12 = 14*12 = 168

 

The speed of the boat is 13 mph

the spped of the current is 1 mph