SOLUTION: A tugboat can pull a boat 24 miles downstream in 2 hours. Going upstream, the tugboat can pull the same boat 16 miles in 2 hours. What is the speed of the tugboat in still water an

Going 24 miles downstream in 2 hours, the tugboat has the effective speed   = 12 miles per hour.

This speed is the sum of the tugboat in still water (u)  and the speed of current (v):

u + v = 12 mph     (1)



Going 16 miles upstream in 2 hours, the tugboat has the effective speed   = 8 miles per hour.

This speed is the difference of the tugboat in still water and the speed of current:

u - v =  8 mph     (2)



Thus you have this system of two equations (1),(2) in two unknowns  

u + v = 12 mph     (1)
u - v =  8 mph     (2)


To solve the system, add two equations (1) and (2)  (both sides). You will get

2u = 12 + 8 = 20  ====>  u =  = 10.


Thus we just found the speed of the tugboat in still water. It is 10 miles per hour.


Then from eq(1),  v = 12 - u = 12 - 10 = 2 mph.


Answer.  The speed of the tugboat in still water is 10 miles per hour.

         The current speed is 2 mph.