Question 473735
Distance = rate*time denoted as d=rt
The boat traveled the same distance of 20 miles both upstream and downstream.
Let s be speed of boat in still water, let c be rate of current.
Downstream boat goes faster so its speed is s+c, Upstream its s - c.
Set up equations:
20 = 4(s+c)
20 = 5(s-c)
Distribute
20 = 4s + 4c
20 = 5s - 5c
Using substitution 
5s - 5c = 4s + 4c
Solve for s: (Subtract 4s on both sides, Add 5c on both sides)
s = 9c
Now substitute 9c in for s:
20 = 4(9c) + 4c
20 = 36c + 4c
20 = 40c
1/2 = c
--> s = 9(1/2) = 9/2 = 4.5
Therefore the boat travels 4.5 mph in still water and the rate of the current is 0.5 mph