Problema Solution
In still water a boat averages 8 miles per hour. It takes the same amount of time to travel 16 miles downstream, with the current, as it does 8 miles upstream, against the current. What is the rate of the water's current
Answer provided by our tutors
let
v = 8 mph the rate of the boat in still water
d1 = 16 mi the distance downstream
d2 = 8 mi the distance upstream
t = the time of the travel upstream = the time of the travel downstream
c = the rate of the water's current
the rate of the boat traveling downstream is: v + c
since rate = distance/time we have
v + c = d1/t
8 +c = 16/t
t = 16/(8 + c)
the rate of the boat traveling upstream is: v - c
v - c = d2/t
8 - c = 8/t
plug t = 16/(8 + c) into the last equation
8 - c = 8/(16/(8 + c))
we find
c = 8/3
c = 2.67 mph
click here to see the step by step solution of the equation
the rate of the water's current is 2.67 mph.