Problema Solution
Bob's boat travels at 14mph in still water. Find the speed of the current if he can go 4 miles upstream in the same time that it takes to go 7 miles downstream.
Answer provided by our tutors
let
v = 14 mph the boats speed in still water
c = the speed of the current
d1 = 4 miles the boat traveled upstream
d2 = 7 miles the boat traveled downstream
t = the time he needs to travel 4 miles upstream = the time he needs to travel 7 miles downstream
downstream speed: v + c
upstream speed: v - c
since speed = distance/time
v + c = d2/t
14 + c = 7/t multiply both sides by t
14t + ct = 7
v - c = d1/t
14 - c = 4/t multiply both sides by t
14t - ct = 4
we have the system of equations
14t + ct = 7
14t - ct = 4
by solving it we find
c = 3.82 mph
click here to see the step by step solution of the system of equations
the speed of the current is 3.82 mph.