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A tugboat goes 160 miles upstream in 20 hours. The return trip downtown takes 10 hours.

Find the speed of the tugboat without a current and the speed of the current.

The speed of the tugboat is what in mph? And what is the speed of the current in mph? (Simplify your answer.)

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Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

Let x be the speed of tugboat without a current and y be the speed of the current.

Upstream speed is "x-y" (because of the stream resistance) and the downstrean speed is "x+y" (the stream helps to move faster). According to the text

                               20(x-y) = 160    

                               10(x+y) = 160

Simplify the system of these two equations dividing both sides of the firsdt equation by 20 and the second one by 10. We will obtain

                                x-y = 8

                                x + y = 16

Addition of two equations gives     2x = 24   or  x =12. Consequently  y = 12 - 8 = 4   or 16-12 =4.

Summarize:  x= 12   y = 4.