document.write( "Question 655436: a bus leaves a city at 12:00 pm and travels 50 miles per hour. A car leaves the same city at 12:30 pm and travels the same route as the bus, but travels at a rate of 60 miles per hour. What time will the car catch up to the bus? \n" ); document.write( "

Algebra.Com's Answer #409135 by josmiceli(19441) $\"\"$ $\"About$

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The bus has a head start of $\"+50%2A.5+=+25+\"$ mi
\n" ); document.write( "Let $\"+d+\"$ = distance car travels until
\n" ); document.write( "it catches the bus
\n" ); document.write( "Let $\"+t+\"$ = time in hours car takes to catch bus
\n" ); document.write( "Start a stopwatch when the car leaves.
\n" ); document.write( "Car's equation:
\n" ); document.write( "(1) $\"+d+=+60t+\"$
\n" ); document.write( "Bus's equation:
\n" ); document.write( "(2) $\"+d+-+25+=+50t+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+60t+-+25+=+50t+\"$
\n" ); document.write( "(2) $\"+10t+=+25+\"$
\n" ); document.write( "(2) $\"+t+=+2.5+\"$
\n" ); document.write( "12:30 + 2.5 hrs = 3:00
\n" ); document.write( "The car catches the bus at 3:00 PM
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+d+=+60%2A2.5+\"$
\n" ); document.write( "(1) $\"+d+=+150+\"$ mi
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+d+-+25+=+50%2A2.5+\"$
\n" ); document.write( "(2) $\"+d+=+25+%2B+125+\"$
\n" ); document.write( "(2) $\"+d+=+150+\"$ mi
\n" ); document.write( "OK \n" ); document.write( "

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