Problema Solution
A woman rows a boat upstream from one point on a river to another point 4miles away in 1 1/2 hours. The returned trip, traveling with the current, takes on 45 minutes. How fast does she row relative to the water, and at what speed is the current flowing?
(Hint: convert the minutes to hours and write the hours in fraction, since the problem is stated mi/h).
Answer provided by our tutors
let
x = the speed of the woman relative to the water
c = the speed of the current flowing
d = 4 miles the distance from one point to the other
t1 = 1 1/2 hours = 3/2 hours the time spent going upstream
(x - c) the speed of the boat going upstream
t2 = 45 min = 45/60 hours = 3/4 hours the time spent traveling with the current
(x + c) the speed of the boat going downstream
the speed = distance/time => distance = speed*time
the distance upstream = distance downstream
(3/2) (x - c) = (3/4) (x + c)
the distance downstream
(3/2) (x - c) = 4
by solving the system of equations
(3/2) (x - c) = (3/4) (x + c)
(3/2) (x - c) = 4
we find
x = 4 mph
c = 4/3 mph
c = 1.33 mph approximately
the speed of the woman relative to the water is 4 mph.
the speed of the current is 1.33 mph approximately.