What are the speed of the current and the speed of the tug relative to the water?

Question

This is from Chapter 5, Exercise 5-3, #14 of Fundamentals of Technical Mathematics (2nd edition): A tug pushes a barge 10 miles upriver in 2.5 hours and downriver the same distance in only one hour. What are the speed of the current and the speed of the tug relative to the water?

Answer 1

distance = speed * time
therefore, speed = distance over time

speed upstream= 10 mi / 2.5 h = 4 mi/h
speed downstream = 10 mi / 1 h = 10 mi/h

The speed of the current is the same on both trips, but acts against the tug on the way up.
T = speed of tug
C = speed of current

T - C = 2.5 mi/h
T + C = 10 mi/h

Two equations, two unknown; go for it.