Problema Solution
A barge takes 4 hours to move (at a constant rate) downstream for 40
miles, helped by a current of 3 miles per hour. If the bargeʹs engines are
set at the same pace, find the time of its return trip against the current.
Answer provided by our tutors
let
v = the speed of the barge in still water
c = 3 mph the speed of the current
d = 40 mi the distance traveled in each direction
t1 = 4 hr the time of the travel downstream
t2 = the time of the travel upstream
the speed of the barge downstream: v + c = v + 3
the speed of the barge upstream: v - c = v - 3
since speed = distance/time we have
moving downstream:
v + 3 = d/t1
v + 3 = 40/4
v + 3 = 10
v = 10 - 3
v = 7 mph
moving upstream:
v - 3 = d/t2
7 - 3 = 40/t2
by solving we find:
t2 = 10 hr
click here to see the step by step solution of the equation:
the time of the return trip against the current is 10 hours.