Problema Solution
a man uses his small motorboat to go 4 miles upstream to his favorite fishing spot. Against the current, the trip takes 2/5 hours. With the current the trip takes 1/5 hours. How fast can the boat travel in still water? What is the speed of the current?
Answer provided by our tutors
let
v = the speed of the sailor in still water
c = the speed of the current
d = 4 mi the distance traveled upstream
t1 = 2/5 hr the time of the travel upstream
t2 = 1/5 hr the time of the travel downstream
since speed = distance/time we have
the rate of the boat traveling upstream is: v - c
v - c = d/t1
v - c = 4/(2/5)
v - c = 10
the rate of the boat traveling downstream is: v + c
v + c = d/t2
v + c =4/(1/5)
v + c = 20
by solving the system of equations
v - c = 10
v + c = 20
we find
v = 15 mph
c = 5 mph
click here to see the step by step solution of the system of equations
the speed of the boat in still water is 15 mph.
the speed of the current is 5 mph.