Problema Solution

A motorboat takes

5

hours to travel

100

mi

going upstream. The return trip takes

2

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


t1 = 5 hr the time of the travel upstream


t2 = 2 hr the time of the travel downstream


d =100 mi the distance traveled in each direction


v = rate of the boat in still water, v>0


r = the rate of the river


we know that speed = distance/time


traveling upstream the rate of the boat is v - r


v - r = d/t1


v - r = 100/5


traveling downstream the rate of the boat is: v + r


v + r = d/t2


v + r = 100/2


by solving the system of equations:


v - r = 100/5


v + r = 100/2

........


click here to see all the system of equations solution steps


........

v = 35 mph


r = 15 mph


The rate of the boat in still water is 35 mph.


The rate of the current is 15 mph.