Problema Solution
On a weekend outing, Manuel rents a motorboat for 8 hours to travel down the river and back. The rental operator tells him to go for 3 hours downstream, leaving 5 hours to return upstream. If the river current flows at a speed of 5 mph, how fast must Manuel travel in order to return in 8 hours? How far downstream did Manuel go before he turned back?
Answer provided by our tutors
let
v = the speed of Manuel in still water
c = 5 mph the current
t1 = 3 hr the time of the travel downstream
t2 = 5 hr the time of the travel upstream
d = the distance traveled in one direction
since distance = speed*time we have:
traveling with the current the speed of the boat is: v + c
(v + c)*t1 = d
(v + 3)*3 = d
traveling against the current the speed of the boat is: v - c
(v - c)*t2 = d
(v - 3)*5 = d
thus we have the following equation:
(v + 3)*3 = (v - 3)*5
by solving we find:
v = 12 mph
click here to see the step by step solution of the equation:
d = (v + 3)*3
d = (12 + 3)*3
d = 45 mi
In order to return in 8 hours Manuel needs to travel with a speed od 12 mph.
Manuel traveled 45 miles downstream before he turned back.