Motorboat traveling given upstream/downstream time, traveled 108km, finding the rate of boat in still water and rate of current

Question

A motorboat takes 3 hours to travel 108km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

First identify quantities
Let s = still water rate
Let c = current rate
D = distance = 108 km
Now write formulas relating the quantities.
The key formula for travel is
Distance = Rate * Time
The key observation is that the rate going downstream is s + c, while the rate going upstream is s - c. So

108 = (s-c)* 3
108 = (s+c)*2
Solve first one for c in terms of s
108 = 3s -3c
3c = 3s - 108
C = s - 36
Substitute into second to find s
108 = (s+c)*2
108 = (s + s-36)*2
108 = 4s -72
4s = 108 + 72 = 180
S = 45
Now substitute to find c
C = 45-36= 9