document.write( "Question 1029944: It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long does it take an unpowered raft to cover this distance? \n" ); document.write( "

Algebra.Com's Answer #644888 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours.
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\n" ); document.write( "\n" ); document.write( " Raft (see this article of Wikipedia)\r
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document.write( "   A raft is any flat structure for support or transportation over water. It is the most basic of boat design, \r\n" );
document.write( "   characterized by the absence of a hull. Although there are cross-over boat types that blur this definition, \r\n" );
document.write( "   rafts are usually kept afloat by using any combination of buoyant materials such as wood, sealed barrels, \r\n" );
document.write( "   or inflated air chambers (such as pontoons), and are typically not propelled by an engine.\r\n" );
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document.write( "It is assumed in this problem that the unpowered raft moves along the river with the current' speed.\r\n" );
document.write( "Therefore, all we need to do is to determine the speed of the current.\r\n" );
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document.write( "Let D be the distance along the river from pier A to pier B.\r\n" );
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document.write( "Let \"u\" be the motorboat speed in still water and \"v\" be the current speed.\r\n" );
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document.write( "When moving upstream, the motorboat has the speed  u-v  (relative to the river's banks),  and it is equal to  .\r\n" );
document.write( "When moving downstream, the motorboat has the speed  u+v  (relative to the river's banks),  and it is equal to  .\r\n" );
document.write( "So, you have these two equations\r\n" );
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document.write( "u + v = ,   (1)\r\n" );
document.write( "u - v = .   (2)\r\n" );
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document.write( "Distract equation (2) from equation (1)  (both sides).  You will get\r\n" );
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document.write( "2v =  =  =  = .\r\n" );
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document.write( "Hence,  v =  = .\r\n" );
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document.write( "Now, the time for the unpowered raft to cover the distance D is \r\n" );
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document.write( " =  = 192 hours.\r\n" );
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document.write( "Answer.  The time for the unpowered raft to get from pier A to pier B is 192 hours.\r\n" );
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