Problema Solution
Julie and eric row their boat (at a constant speed of 7 miles per hour)48 miles downstream for 6 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the current.
Answer provided by our tutors
let
v = 7 mph the rate of the boat in still water
c = the rate of the current
d = 48 mi the distance traveled in one direction
t1 = 6 hr time of the travel downstream
t2 = 8 hr the time of the return trip upstream
the boats speed downstream: v + c
the boats speed upstream: v - c
since speed = distance/time => distance = speed*time
traveling downstream
(v + c)t1 = d
(7+ c)6 = 48 divide both sides by 6
7 + c = 8
c = 8 - 7
c = 1 mph
traveling upstream
(7 - c)*8 = 48 divide both sides by 8
7 - c = 6
c = 7 - 6
c = 1 mph
the rate of the current is 1 mph.