Problema Solution
A small motorboat travels
16 mph in still water. It takes
1 hour longer to travel
58 miles going upstream than it does going downstream. Find the rate of the current.
Answer provided by our tutors
Let
v = 16 mph the speed of the boat in still water
c = the current of the stream
d = 58 miles the distance traveled in one direction
t = the time of the travel downstream
t + 1 = the time of the travel upstream
the speed upstream is: v - c
the speed downstream is: v + c
Since speed = distance/time => time*speed = distance
t(v + c) = d
t(16 + c) = 58
t = 58/(16 + c)
(t + 1)(v - c) = d
(t + 1)(16 - c) = 58
lets plug t = 58/(16 + c) into the last equation
(58/(16+ c) + 1)(16 - c) = 58
........
........
c = 2.17 mph
The rate of the current is 2.17 mph.