Aboat traveled 192 miles each way downstream and back. the trip downstream took 8 hours. the trip back took 24 hours. what is the speed of the boat in still water? what is the speed of the current?

In this problem, 2 equations could be formed.
The distance would be equal in either direction which is 192 miles. They would differ in speed and time. 

let x= speed of current and y = speed of still water

Downstream: 8(x + y) = 192 ---> eq 1
Upstream: 24(x - y) = 192 ---> eq 2

Simplifying,

eq 1: x + y = 24
eq 2: x - y = 8
  
  x + y = 24
-
  x -  y = 8

       2y = 16
         y = 8

Then, 

x + 8 = 24
x = 16

The answer is

speed of still water = 8 mph
speed of current = 16 mph