document.write( "Question 1111808: I have to walk a distance of 24km. If I increase my usual rate of walking by 2km/h, I can reduce the time taken by 1 hour.
\n" ); document.write( "a) find my usual rate of walking
\n" ); document.write( "b) if I can reduce my usual rate of walking by 2km/ h, how long does it take me to walk 24km? \n" ); document.write( "

Algebra.Com's Answer #726825 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let \"r\" be your usual rate, and t be the time to walk 24 km at this rate.\r\n" );
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document.write( "Then\r\n" );
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document.write( "rt = 24                 (1)\r\n" );
document.write( "(r+2)*(t-1) = 24.       (2)\r\n" );
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document.write( "Transform eq(2) in this way:\r\n" );
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document.write( "rt + 2t - r - 2 = 24.   (3)\r\n" );
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document.write( "Take into account that 24 = rt in accordance with (1).  So you can cancel the terms rt and 24 in both sides of the equation (3) to get\r\n" );
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document.write( "2t - r - 2 = 0,   or simply   r = 2t-2 = 2*(t-1).\r\n" );
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document.write( "Next substitute this expression for r,  r = 2*(t-1),  into eq(1)  to get\r\n" );
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document.write( "2(t-1)*t = 24,   or  t*(t-1) = 12.\r\n" );
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document.write( "Further, you can solve the last equation for t  as a quadratic equation,  or simply \"to guess\" the solution t = 4.\r\n" );
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document.write( "So, the answer to the question  a)  is   t = 4 hours  (your usual time)  and  r =  = 6 km/h  (your usual rate).\r\n" );
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document.write( "Having this, you can easily resolve b) on your own.\r\n" );
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\n" ); document.write( "To see other similar solved problems, look into the lesson\r
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