Problema Solution
A boat travels downstream between two points on a river 20 miles apart in 2 hours. The return trip against the current takes 3.5 hours. What is the boats speed, and how fast does the current in the river flow?
Answer provided by our tutors
let
v = the rate of the boat in still water
c = the rate of the current
d = 20 mi the distance traveled in one direction
t1 = 2 hr time of the travel downstream
t2 = 3.5 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)2 = 20
traveling upstream
(v - c)3.5 = 20
by solving the system of equations
(v + c)2 = 20
(v - c)3.5 = 20
we find
c = 2.14 mph
v = 7.86 mph
click here to see the step by step solution of the system of equations