Problema Solution
Liam is planning a three hour trip down the East River and back to his starting point. He knows that he can paddle in still water at 3 mi/h and that the rate of the current is 2 mi/h. How much time can he spend going downstream? How far down stream can he travel?
Answer provided by our tutors
let
v = 3 mph the speed of Liam in still water
c = 2 mph the rate of the current
t1 = the time going downstream
t2 = the time going upstream
d = the distance in one way
paddling downstream
(v + c)*t1 = d
(3 + 2)t1 = d
5 t1 = d
paddling upstream
(v - c)*t2 = d
(3 - 2)t2 = d
t2 = d
the total time
t1 + t2 = 3
by solving the system of equations
5 t1 = d
t2 = d
t1 + t2 = 3
and since t2 = d we can reduce it to the system
5*t1 = t2
t1 + t2 = 3
we find
t1 = 0.5 h = 30 min
t2 = 2.5 h = 2 h 30 min
click here to see the step by step solution of the system of two equations
the distance going downstream is 2.5 miles.
he spends 30 min paddling downstream.