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


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the rate of the boat in still water is 12 mph.


the rate of the current is 3 mph.