A boat takes 5 hr to go 25 mi upstream. It can go 50 mi downstream in the same time. Find the rate of the current and the rate of the boat in still water if x = the rate of the boat in still water and y = the rate of the current. d x + y Downstream Upstream 5 The rate of the current is
we have that
x -----> the rate of the boat in still water
y -----> the rate of the current
Downstream
(x+y)5=d
(x+y)5=50
5x+5y=50 ------> equation A
Upstream
(x-y)5=25
5x-5y=25 ------> equation B
solve the system of equations
Adds equation A and equation B
5x+5y=50
5x-5y=25
----------------
10x=75
x=7.5 miles per hour
Find the value of y
5(7.5)-5y=25
5y=37.5-25
5y=12.5
y=2.5 miles per hour
therefore
The rate of the current is 2.5 miles per hour