Question

In still​ water, a boat averages 18 18 miles per hour. it takes the same amount of time to travel 16 miles 16 miles ​downstream, with the​ current, as it does 8 8 miles​ upstream, against the current. what is the rate of the​ water's current?

Answer 1

The current is 6 miles per hour.
   Let's create a few equations:
 Traveling with the current:
 (18 + c)*t = 16

   Traveling against the current:
 (18 - c)*t = 8

   Let's multiply the 2nd equation by 2
 (18 - c)*t*2 = 16

   Now subtract the 1st equation from the equation we just doubled.
 (18 - c)*t*2 = 16
 (18 + c)*t = 16

   (18 - c)*t*2 - (18 + c)*t = 0
 Divide both sides by t
 (18 - c)*2 - (18 + c) = 0

   Now solve for c
 (18 - c)*2 - (18 + c) = 0
 36 - 2c - 18 - c = 0
 36 - 2c - 18 - c = 0
 18 - 3c = 0
 18 = 3c
  6 = c

   So the current is 6 mph.
   Let's verify that.
 (18 + 6)*t = 16
 24*t = 16
 t = 16/24 = 2/3

   (18 - 6)*t = 8
 12*t = 8
 t = 8/12 = 2/3

   And it's verified.