document.write( "Question 1129303: It takes 5 hours for a boat to travel 80 miles downstream. The boat can travel the same distance back upstream in 8 hours. Find the speed of the boat in still water and the speed of the current. \n" ); document.write( "

Algebra.Com's Answer #745864 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Against the current the effective speed (the speed relative to the river bank) is\r\n" );
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document.write( "u - v =  = 10  miles per hour.     (1)   (u = the speed of the boat in still water;  v = the speed of the current)\r\n" );
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document.write( "With the current, the effective speed is\r\n" );
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document.write( "u + v =  =  16 miles per hour.     (2)\r\n" );
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document.write( "Add equations (1) and (2)\r\n" );
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document.write( "2u = 16 + 10 = 26  ====>  u = 26/2 = 13 mph is the speed of the boat in still water.    ANSWER\r\n" );
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document.write( "Subtract eq(1) from eq(2)\r\n" );
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document.write( "2v = 16 - 10 = 6  ====>  v = 6/2 = 3 mph  is the speed of the current.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from this solution and the tnings to memorize are :\r
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document.write( "    1.  The effective speed of a boat traveling with    a current is the sum        of the two speeds.\r\n" );
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document.write( "    2.  The effective speed of a boat traveling against a current is the difference of the two speeds.\r\n" );
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document.write( "    3.  It gives a system of two equations in two unknowns, which fits very well for solving by the elimination method.\r\n" );
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