Let
x---------> the rate of the boat in still water in mph
y--------> the rate of the current in mph
we know that
Upstream
[tex] rate=\frac{20}{4} \\\\ rate=5mph [/tex]
[tex] x-y=5 [/tex] equation [tex] 1 [/tex]
Downstream
[tex] rate=\frac{32}{4} \\\\ rate=8mph [/tex]
[tex] x+y=8 [/tex] equation [tex] 2 [/tex]
Adds equation [tex] 1 [/tex] and equation [tex] 2 [/tex]
[tex] x-y=5\\ x+y=8\\ -----\\ 2x=13\\ x=6.5mph [/tex]
Find the value of y
[tex] x+y=8\\ y=8-x\\ y=8-6.5\\ y=1.5 mph [/tex]
therefore
the answer is
the rate of the boat in still water is [tex] 6.5 mph [/tex]
the rate of the current is [tex] 1.5 mph [/tex]
