SOLUTION: A motor boat traveling with the current went 12 mi in 1 h. Against the current, it took 2 h to travel the same distance. Find the rate of the boat in calm water and the rate of the

Algebra ->  Test -> SOLUTION: A motor boat traveling with the current went 12 mi in 1 h. Against the current, it took 2 h to travel the same distance. Find the rate of the boat in calm water and the rate of the      Log On


   

Question 332537: A motor boat traveling with the current went 12 mi in 1 h. Against the current, it took 2 h to travel the same distance. Find the rate of the boat in calm water and the rate of the current.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A motor boat traveling with the current went 12 mi in 1 h.
Against the current, it took 2 h to travel the same distance.
Find the rate of the boat in calm water and the rate of the current.
:
Let s = boat speed in calm water
Let c = rate of the current
then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
:
Write a dist equation for each trip: dist = time * effective speed
1(s + c) = 12
2(s - c) = 12
:
On the first equation divide both sides by 1
On the second equation divide both sides by 2
:
s + c = 12
s - c = 6
------------adding, eliminates c, find s
2s = 18
s = 9 mph, boat speed in calm water
Find c
s + c = 12
9 + c = 12
c = 12 - 9
c = 3 mph is the current
:
:
Check solutions in the original 2nd equation
2(9 - 3) = 12