document.write( "Question 1089509: a cruise ship made a trip of 100 mi in 8 h the ship traveled the first 40 mi at a constant rate before increasing its speed by 5 mph another 60 mi was traveled at the increased speed fond the rate of the cruise ship for the first 40 mi? \n" ); document.write( "

Algebra.Com's Answer #703836 by ikleyn(52775) $\"\"$ $\"About$

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\n" ); document.write( "Answer. The rate of the cruise ship for the first 40 mi is 10 miles per hour.\r
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\n" ); document.write( "\n" ); document.write( "Check. $\"40%2F10+%2B+60%2F%2810%2B5%29\"$ = 4 + 4 = 8 hours. ! Correct !\r
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document.write( "Let \"r\" be the slower rate of the cruise ship, in miles per hour.\r\n" );
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document.write( "Then the faster speed is (r+5) miles per hour.\r\n" );
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document.write( "The time spent to cover 40 miles at the rate \"r\" mph is  hours.\r\n" );
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document.write( "The time spent to cover 60 miles at the rate (r+5) mph is  hours.\r\n" );
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document.write( "The condition says that the total time is 8 hours:\r\n" );
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document.write( " +  = 8.\r\n" );
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document.write( "To solve this equation, multiply both sides by r*(r+5). You will get\r\n" );
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document.write( "40*(r+5) + 60*r = 8r*(r+5).\r\n" );
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document.write( "Simplify and solve for \"r\".\r\n" );
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document.write( "40r + 200 + 60r = 8r^2 + 40r,\r\n" );
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document.write( "8r^2 - 60r - 200 = 0,   ====>  (divide both sides by 4)  ====>\r\n" );
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document.write( "2r^2 - 15r - 50 = 0,\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "Only positive root r= 10 works.\r\n" );
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document.write( "Answer. The rate of the cruise ship for the first  40 mi  is  10 miles per hour.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I apologize for my words in previous version.\r
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