R = rate of boat no current
C = rate of current
120 = 20(R-C)
120 = 5(R+C)
6 = (R-C)
24 = (R+C)
30 = +2R
15 = R
24-15 = -15 +15+C
9 = C
speed of tugboat is 15 mph, and the current is 9 mph.
It would help if you told us what the problem itself says! Are you saying that the boat goes upstream 120 miles in 20 hours and goes downstream 120 miles in 5 hours?
It should be easy for you to check it yourself. If the boat has a normal speed of 15 mph and the current is 9 mph, the actual speed of the boat upstream, relative to the shore, is 15- 9= 6 mph. In 20 hours, the boat will have gone 6(20)= 120 miles. Downstream, the actual speed, relative to the shore, is 15+9= 24 mph. In 5 hours the boat will have gone 5(24)= 120 mi. Looks good.
The problem was not in asking for help, but not actually posting a question. For instance you found values for R and C. They mean nothing on their own. What is the actual problem statement for this question?
Your post is a mystery. If you want help you're going to have to give more information.
-Dan