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.