document.write( "Question 676175: a car leaves town at 30 mph, tow hours later another car leaves same place, going the same direction at a speed of 42 mph. How many hours will the second car be driven before it catches up?
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Algebra.Com's Answer #420214 by josmiceli(19441) $\"\"$ $\"About$

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How much of a head start does the 1st car get?
\n" ); document.write( " $\"+d%5B1%5D+=+30%2A2+\"$
\n" ); document.write( " $\"+d%5B1%5D+=+60+\"$ mi
\n" ); document.write( "Now start a stop watch when the 2nd car leaves
\n" ); document.write( "Let $\"+t+\"$ = time on stopwatch when 2nd car catches first car
\n" ); document.write( "Let $\"+d+\"$ = distance 2nd car travels until it catches 1st car
\n" ); document.write( " $\"+d+-+60+\"$ = distance 1st car travels
\n" ); document.write( "-------------------
\n" ); document.write( "Equation for 1st car:
\n" ); document.write( "(1) $\"+d+-+60+=+30t+\"$
\n" ); document.write( "Equation for 2nd car:
\n" ); document.write( "(2) $\"+d+=+42t+\"$
\n" ); document.write( "--------------
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+42t+-+60+=+30t+\"$
\n" ); document.write( "(1) $\"+12t+=+60+\"$
\n" ); document.write( "(1) $\"+t+=+5+\"$
\n" ); document.write( "The 2nd car catches the 1st car in 5 hrs
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+d+=+42t+\"$
\n" ); document.write( "(2) $\"+d+=+42%2A5+\"$
\n" ); document.write( "(2) $\"+d+=+210+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+d+-+60+=+30t+\"$
\n" ); document.write( "(1) $\"+210+-+60+=+30t+\"$
\n" ); document.write( "(1) $\"+150+=+30t+\"$
\n" ); document.write( "(1) $\"+t+=+5+\"$
\n" ); document.write( "OK
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