document.write( "Question 1075485: A tourist traveled on a motorboat against the current for 25 km. And then returned back on a raft. In the boat the tourist traveled for 10 hours less than on the raft. Find the speed of the current if the speed of the motorboat in still water is 12 km/hour. Show your work! \n" ); document.write( "

Algebra.Com's Answer #690137 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A tourist traveled on a motorboat against the current for 25 km. And then returned back on a raft.
\n" ); document.write( "In the boat the tourist traveled for 10 hours less than on the raft.
\n" ); document.write( "Find the speed of the current if the speed of the motorboat in still water is 12 km/hour.
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document.write( "Let x be the speed of the current, in km/h units.\r\n" );
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document.write( "Then the speed of the boat traveling against the current is (12-x) km/h.\r\n" );
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document.write( "The time spent traveling 25 miles against the current is  hours.\r\n" );
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document.write( "The time spent rafting 25 miles (with the current) is  hours.\r\n" );
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document.write( "The equation is \r\n" );
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document.write( " = 10.\r\n" );
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document.write( "To solve it, multiply both sides by x*(12-x). You will have\r\n" );
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document.write( "25*(12-x) - 25x = 10x*(12-x),\r\n" );
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document.write( "300 - 25x - 25x = ,\r\n" );
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document.write( " = 0,\r\n" );
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document.write( " = 0,\r\n" );
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document.write( "(x-2)*(x-15) = 0. \r\n" );
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document.write( "The roots are x= 2  and  x= 15.\r\n" );
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document.write( "Since 12-x must be positive, the only root x = 2 survives.\r\n" );
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document.write( "Answer.  The current speed is 2 km/h.\r\n" );
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document.write( "Check.  The time traveling against the current  = 2.5 hours.\r\n" );
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document.write( "        The time rafting is  = 12.5 hours.\r\n" );
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document.write( "        12.5 - 2.5 = 10 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( "    - Wind and Current problems solvable by quadratic equations \r
\n" ); document.write( "\n" ); document.write( "    - Unpowered raft floating downstream along a river\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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