SOLUTION: My problem is a word problem that goes like this: A tugboat goes 120 miles upstream in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tug boat without a

Question 632568: My problem is a word problem that goes like this: A tugboat goes 120 miles upstream in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tug boat without a current, and, find the speed of the current.
So, I have two variables x= tugboat speed, and y = current speed, I believe that this is basically a rate, time, distance type of problem. I tried to solve it like this: 120x20=2400 multiply
120x10=1200 add
=3600/2=1800 divide by 2
1800-2400=-600, 1800-1200=600, I know that this is incorrect,as it is impossible for a tugboat to go -600 mph, or for a river current to move at 600 mph. I saw a similar problem on this sight, but I think the asker formatted the problem improperly, because the answer was only one part, and the problem requires a two part answer, and it just does not fit this particular problem either. Can you help me understand how to solve this problem? Thanks

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A tugboat goes 120 miles upstream in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tug boat without a current, and, find the speed of the current.
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Upstream DATA:
distance = 120 miles ; time = 20 hrs ; rate = d/t = 120/20 = 6 mph
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Downstream DATA:
distance = 120 miles ; time = 10 hrs ; rate = d/t = 120/10 = 12 mph
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Equations:
b + c = 12 mph
b - c = 6 mph
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Add and solve for "b":
2b = 18 mph
boat speed = 9 mph
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Solve for "c":
b + c = 12 mph
9 + c = 12
current speed = 3 mph
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Cheers,
Stan H.
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