Problema Solution
A motorboat takes 5 hours to travel 200 miles going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer provided by our tutors
let
v = the rate of the boat in still water
c = the rate of the current
d = 200 mi the distance traveled in each direction
t1 = 5 hr the time of the travel upstream
t2 = 4 hr the time of the travel downstream
traveling upstream the rate of the boat is: v - c
v - c = d/t1
v - c = 200/5
v - c = 40
traveling downstream the rate of the boat is: v + c
v + c = d/t2
v + c = 200/4
v + c = 50
by solving the system of equations:
v - c = 40
v + c = 50
........
........
v = 45 mph
c = 5 mph
the rate of the boat in still water is 45 mph.
the rate of the current is 5 mph.