document.write( "Question 1070600: The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. he has a boat in mind, but he can only test in on a... show more he speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. he has a boat in mind, but he can only test in on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator's needs? \n" ); document.write( "

Algebra.Com's Answer #685653 by ikleyn(52878) $\"\"$ $\"About$

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\n" ); document.write( "The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. he has a boat in mind, but he can only test in on a... show more he speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. he has a boat in mind, but he can only test in on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator's needs?
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\n" ); document.write( "\n" ); document.write( "Let me reformulate the problem equivalently in more convenient terms.\r
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document.write( "    The round trip of 22.5 miles upstream and the same distance downstream takes 9 hours.\r\n" );
document.write( "    Find the speed of the boat in still water if the current rate is 6 mph.\r\n" );
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document.write( "Let u be the speed of the boat in still water.\r\n" );
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document.write( "Then  the speed of the boat traveling upstream   is (u-6) mph, \r\n" );
document.write( "while the speed             traveling downstream is (u+6) mph.\r\n" );
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document.write( "The \"time\" equation is\r\n" );
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document.write( " = 9.\r\n" );
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document.write( "Solve for u. For it, multiply both sides by 2*(u-6)*(u+6). You will get\r\n" );
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document.write( "45(u+6) + 45*(u-6) = ,   --->\r\n" );
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document.write( "90u = ,\r\n" );
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document.write( " = 0   --->   \r\n" );
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document.write( " = 0  --->  (u-9)*(u+4) = 0  --->   \r\n" );
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document.write( "The only positive root is u = 9.\r\n" );
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document.write( "Answer.  The speed of the boat in still water is 9 mph.\r\n" );
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document.write( "Check.    = 9 hours.   Correct !!\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a typical and standard Upstream and Downstream round trip word problem.\r
\n" ); document.write( "\n" ); document.write( "You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons \r
\n" ); document.write( "\n" ); document.write( "    - Wind and Current problems \r
\n" ); document.write( "\n" ); document.write( "    - More problems on upstream and downstream round trips \r
\n" ); document.write( "\n" ); document.write( "    - Selected problems from the archive on the boat floating Upstream and Downstream \r
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\n" ); document.write( "\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the section \"Word problems\", the topic \"Travel and Distance problems\".\r
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