Problema Solution
If Joe rowed his boat with the current 3 hours down stream, and the same trip took 5 hours upstream against the current, what is the rate of the boat in still water AND the rate of the current if the distance one-way was 45 miles?
Answer provided by our tutors
let
d = 45 mi the distance in one direction
t1 = 3 hr the time down stream
t2 = 5 hr the time up stream
c = the rate of the current, c>0
v = the speed of the boat in still water, v>0
rowing with the current the speed of the boat is: v + c
rowing against the current the speed of the boat is: v - c
since speed = distance/time follows distance = speed*time
rowing with the current:
(v + c)t1 = d
(v + c)*3 = 45
rowing against the current:
(v - c)*5 = 45
by solving the system of equations:
(v + c)*3 = 45
(v - c)*5 = 45
we find:
c = 3 mph
v = 12 mph
click here to see the step by step solution of the system of equations:
the rate of the boat in still water is 12 mph.
the rate of the current is 3 mph.