Let u represent the rate of the boat in still water and 
let y represent the rate of the current. 


Then  the  effective speed downstream  is  u+v  miles per hour,
while the  effective speed upstream    is  u-v  miles per hour.


    // It is first major point you need understand and use in this sort of problems.



Now, "speed" equation for boat floating downstream is the distance divided by time downstream

     = u + v        (where 1/3 represents 20 minutes = 1/3 of an hour)

or  18 = u + v.      (1)



Next, "speed" equation for boat floating upstream is the distance divided by time  uptream


     = u - v        (where 1/2 represents 30 minutes = 1/2 of an hour)

or  12 = u - v.      (2)


    // It is the second major point in solving such problems: you must understand and write these equation automatically !



So, you have this system of equations for u and v

    u + v =  18      (3)
    u - v =  12      (4)


Now add equations (3) and (4) to eliminate "v". You will get

    2u = 18 + 12 = 30.     

Hence,  u =  = 15.


Thus you just found the boat' speed in still water. It is 15 miles per hour.


Next, you can find the current rate from equation (3)  

    v = 18 - u = 18 - 15 = 3 miles per hour.


Answer.  The boat' speed in still water is 15 miles per hour.

         The current speed is 3 miles per hour.



Solved.  I advise you to make the check on your own.

         After making the check, you will understand the problem and the solution MUCH better.

        Do not pack more than one problem per post.

                    N E V E R