document.write( "Question 785534: Mary drove to the train station and back. It took two hours less time to get there than it did to get back. The average s[ed on the trip there was 50 mph. The average speed on the way back was 30mph. How many hours did the trip there take? \n" ); document.write( "

Algebra.Com's Answer #477690 by KMST(5328) $\"\"$ $\"About$

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$\"t\"$ = hours takem for the round trip
\n" ); document.write( " $\"r\"$ = hours taken for the return trip
\n" ); document.write( " $\"t=r%2B%28r-2%29\"$ --> $\"t=2r-2\"$ --> $\"t%2B2=2r\"$ --> $\"r=%28t%2B2%29%2F2\"$
\n" ); document.write( " $\"d\"$ = distance to the station = distance traveled back from the station
\n" ); document.write( "For the round trip we know that
\n" ); document.write( " $\"50t=2d\"$
\n" ); document.write( "For the return trip we know that
\n" ); document.write( " $\"d=30%28%28t%2B2%29%2F2%29\"$ --> $\"d=30%28t%2B2%29%2F2\"$ --> $\"d=15%28t%2B2%29\"$ --> $\"d=15t%2B30\"$
\n" ); document.write( "Substtituting that expression for $\"d\"$ into $\"50t=2d\"$ we get
\n" ); document.write( " $\"50t=2%2A%2815t%2B30%29\"$ --> $\"50t=30t%2B60\"$ --> $\"50t-30t=60\"$ --> $\"20t=60\"$ --> $\"highlight%28t=3%29\"$
\n" ); document.write( "Unfortunately, what that means for the trip distances and speeds is scary:
\n" ); document.write( " $\"2d=50%2A3\"$ --> $\"2d=150\"$ --> $\"d=150%2F2=75\"$
\n" ); document.write( " $\"r=%283%2B2%29%2F2\"$ --> $\"r=2.5\"$
\n" ); document.write( "If the trip back took 2.5 hours and the trip to the station took 2hours less,
\n" ); document.write( " $\"2.5h-2h=0.5h\"$ ,
\n" ); document.write( "Mary drove the 75 miles to the station in 0.5 hours.
\n" ); document.write( "Her average speed when going to the station was
\n" ); document.write( " $\"75miles%2F%28%220.5+hours%22%29=150mph\"$ \n" ); document.write( "

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