SOLUTION: A columbia river tugboat can go 12 mph in still water. It travels up the river 30 miles and back 30 miles in a total time of 6 hours. What is the speed of the current?

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Question 618536: A columbia river tugboat can go 12 mph in still water. It travels up the river 30 miles and back 30 miles in a total time of 6 hours. What is the speed of the current?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A Columbia river tugboat can go 12 mph in still water.
It travels up the river 30 miles and back 30 miles in a total time of 6 hours.
What is the speed of the current?
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Let c = speed of the current
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Write a time equation; time = dist/speed
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Time downstream + Time up = 6 hrs
30%2F%28%2812-c%29%29 + 30%2F%28%2812%2Bc%29%29 = 6
multiply by (12-c)(12+c), results:
30(12+c) + 30(12-c) = 6(12-c)(12+c)
360 + 30c + 360 - 30c = 6(144 - c^2)
720 = 864 - 6c^2
6c^2 = 864 - 720
6c^2 = 144
Divide both sides by 6
c^2 = 24
c = sqrt%2824%29
c = 4.9 mph is the current
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Check this:
30%2F7.1 + 30%2F16.9 = 6.00