document.write( "Question 1208878: A man calculates that if he continues at the present speed, to drive the remaining 100km of his trip, he will arrive 30 minutes late. In order to arrive on time, he must travel at an average rate of 10 kph faster. What is his present speed? \n" ); document.write( "

Algebra.Com's Answer #847386 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A man calculates that if he continues at the present speed, to drive the remaining 100km
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document.write( "Let v be the man's present speed, in kilometers per hour.\r\n" );
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document.write( "Then the other, hypothetical speed is (v+10) km/h.\r\n" );
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document.write( "The time to drive 100 km at the speed v      km/h  is    hours.\r\n" );
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document.write( "The time to drive 100 km at the speed (v+10) km/h  is    hours.\r\n" );
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document.write( "The problem says that time    is 30 minutes, or 1/2 of an hour less than time  .\r\n" );
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document.write( "So, we write this time equation\r\n" );
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document.write( "    -  =   of an hour.\r\n" );
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document.write( "At this point, the setup is complete.\r\n" );
document.write( "To solve this equation, multiply its terms by 2v*(v+10) in both sides.\r\n" );
document.write( "You will get\r\n" );
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document.write( "    100*2*(v+10) - 100*2*v = v*(v+10),\r\n" );
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document.write( "    200v + 2000 - 200v = v^2 + 10v\r\n" );
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document.write( "    v^2 + 10v - 2000 = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (v+50)*(v-40) = 0.\r\n" );
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document.write( "This equation has two roots,  v= -50  and v= 40.\r\n" );
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document.write( "Since v should be positive, due to its meaning, we accept the positive root v= 40 km/h\r\n" );
document.write( "and deny the negative root.\r\n" );
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document.write( "So, the ANSWER  to the problem is that the present speed of driving is 40 km/h.\r\n" );
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document.write( "CHECK.  Driving time at the present speed is   = 2 hours.\r\n" );
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document.write( "        Driving time at the speed of 40+10 = 50 km/h  is   = 2 hours.\r\n" );
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document.write( "        The difference of the two driving times is 1/2 of an hour, or precisely 30 minute,\r\n" );
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document.write( "        which confirms that the answer is correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This solution method (using time equation) is a standard approach for solving similar problems.\r
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