Question 334011: A boat traveled 120 miles downstream and back. The trip downstream took 6 hours. The trip back took 15 hours. Find the speed of the boat in still water and the speed of the current.
I know the answer is that the boat in still water is 14 miles per hour and the current is 6 miles per hour (I looked at the answer sheet! Shhhh!) but i need to know how to solve it!
Help? Thank you!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A boat traveled 120 miles downstream and back.
The trip downstream took 6 hours.
The trip back took 15 hours.
Find the speed of the boat in still water and the speed of the current.
:
Let s = speed in still water
Let c = speed of the current
then
(s+c) = effective speed downstream
and
(s-c + effective speed upstream
:
Write a distance equation for each trip; dist = time * effective speed
6(s+c) = 120
15(s-c) = 120
Simplify both these equations, divide the 1st by 6; divide the 2nd by 15, results:
s + c = 20
s - c = 8
--------------adding these equations eliminate c, find s
2s = 28
s = 14 mph speed in still water
then
s + c = 20
14 + c = 20
c = 20 - 14
c = 6 mph is the current
:
:
Check the solutions in the original equations to be sure
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