SOLUTION: A boat can travel 5 miles upstream and 5 miles downstream in a total of 6 hours. If the speed of the current is 2 miles per hour, what is the speed of the boat in still water?
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Question 91765: A boat can travel 5 miles upstream and 5 miles downstream in a total of 6 hours. If the speed of the current is 2 miles per hour, what is the speed of the boat in still water? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A boat can travel 5 miles upstream and 5 miles downstream in a total of 6 hours. If the speed of the current is 2 miles per hour, what is the speed of the boat in still water?
:
Let s = speed in still water
Then
(s+2) = speed down-stream
and
(s-2) = speed up-stream
:
Write a time equation; Time = dist/speed
:
Time up-stream + time down-stream = 6 hrs + = 6
:
Multiply equation by (s-2)(s+2) and you have:
5(s+2) + 5(s-2) = 6(s-2)(s+2)
:
5s + 10 + 5s - 10 = 6(s^2 - 4)
:
5s + 5s + 10 - 10 = 6s^2 - 24
:
10s = 6s^2 - 24
:
0 = 6s^2 - 10s - 24
:
Simplify divide equation by 2 and you have:
3s^2 - 5s - 12 = 0
:
Factors to
(3s + 4 )(s - 3) = 0
:
s = +3 mph in still water, (it's the positive solution we want here)
:
:
Check using time: speed upstream (3-2)= 1 mph; speed down (3+2) = 5 mph
5/1 = 5 hrs upstream
5/5 = 1 hr downstream
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total 6 hrs as given
