Problema Solution

don Williams uses his small motorboat to go 3 miles upstream to his favorite spot. Against the current, the trip takes 3/5 hour.With the current it takes 1/5 hour. HOw fast can the boat travel in still water? what is the speed of the current?

Answer provided by our tutors

let


d = 3 mi the distance of the travel in one direction

t1 = 3/5 hr the time of the travel against the current

t2 = 1/5 hr the time of the travel with the current

c = the speed of the current, c>0

v = the speed of the boat in still water, v>0


since speed = distance/time follows speed*time = distance


traveling upstream the speed of the boat is: v - c


(v - c)t1 = d


(v - c)(3/5) = 3 multiply both sides by 5/3


v - c = 5


traveling downstream the speed of the boat is: v + c


(v + c)t2 = d


(v + c)(1/5) = 3 multiply both sides by 5


v + c = 15


by solving the system of equations


v - c = 5

v + c = 15


we find


v = 10 mph


c = 5 mph


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The speed of the boat in still water is 10 mph.


The speed of the current is 5 mph.