document.write( "Question 737528: A red car is traveling at 55 mph. A blue car is traveling at 65 mph. The cars are 305 miles apart. The cars started at the same spot at different times. The cars have been driving for 5 hours. Which system of equations could be used to solve for the total driving time of the red car (r) and the total driving time of the blue car (b)? \n" ); document.write( "

Algebra.Com's Answer #450418 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+d+\"$ = distance red car has traveled
\n" ); document.write( " $\"+305+-+d+\"$ = distance blue car has traveled
\n" ); document.write( " $\"+r+\"$ = time for red car
\n" ); document.write( " $\"+b+\"$ = time for blue car
\n" ); document.write( "-----------------------
\n" ); document.write( "One of the cars must have been traveling for
\n" ); document.write( " $\"+5+\"$ hrs, the other for less time
\n" ); document.write( "-----------------------
\n" ); document.write( "red car:
\n" ); document.write( "(1) $\"+d+=+55%2Ar+\"$
\n" ); document.write( "blue car:
\n" ); document.write( "(2) $\"+305+-+d+=+65%2Ab+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "(2) = $\"+d+=+305+-+65b+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+55r+=+305+-+65b+\"$
\n" ); document.write( " $\"+11r+%2B+13b+=+61+\"$
\n" ); document.write( "The red car had to be the one traveling for $\"+5+\"$ ,
\n" ); document.write( "since $\"+13%2A5+=+65+\"$ is too much, so
\n" ); document.write( " $\"+11%2A5+%2B+13b+=+61+\"$
\n" ); document.write( " $\"+13b+=+61+-+55+\"$
\n" ); document.write( " $\"+13b+=+6+\"$
\n" ); document.write( " $\"+b+=+6%2F13+\"$ hrs
\n" ); document.write( "The red car drove for 5 hrs, the blue car drove for 6/13 hrs
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+d+=+55%2Ar+\"$
\n" ); document.write( "(1) $\"+d+=+55%2A5+\"$
\n" ); document.write( "(1) $\"+d+=+275+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+305+-+d+=+65%2Ab+\"$
\n" ); document.write( "(2) $\"+305+-+275+=+65%2A%286%2F13%29+\"$
\n" ); document.write( "(2) $\"+30+=+30+\"$
\n" ); document.write( "OK\r
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