Problema Solution
A motorboat takes 4 hours to travel 192mi going upstream. The return trip takes 3 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
t1 = 4 hr time of the travel upstream
d = 192 mi upstream travel distance
t2 = 3 hr the time of the return trip downstream
the boats speed downstream: v + c
the boats speed upstream: v - c
since speed = distance/time we have
travelling downstream
v + c = d/t2
v + c = 192/3
v + c = 64
travelling upstream
v - c = d/t1
v - c = 192/4
v - c = 48
by solving the system of equations
v + c = 64
v - c = 48
we find
v = 56 mph
c = 8 mph
click here to see the step by step solution of the system of equations
the rate of the boat in still water is 56 miles per hour.
the rate of the current is 8 miles per hour.