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
click here to see the step by step solution of the system of equations
The speed of the boat in still water is 10 mph.
The speed of the current is 5 mph.