document.write( "Question 944976: I need help solving this word problem. You drove 370 miles in 6 hours. You drove 70 mph on the highway and 45 mph on the back roads. How many hours did you spend on each? \n" ); document.write( "

Algebra.Com's Answer #576212 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = time spent on highway in hours
\n" ); document.write( " $\"+6+-+t+\"$ = time spent on back road in hours
\n" ); document.write( "Let $\"+d+\"$ = distance traveled on highway in miles
\n" ); document.write( " $\"+370+-+d+\"$ = distance traveled on back roads in miles
\n" ); document.write( "--------------------------------------------------
\n" ); document.write( "On highway:
\n" ); document.write( "(1) $\"+d+=+70t+\"$
\n" ); document.write( "On back roads:
\n" ); document.write( "(2) $\"+370+-+d+=+45%2A%28++6+-+t+%29+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+370+-+d+=+270+-+45t+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+370+-+70t+=+270+-+45t+\"$
\n" ); document.write( "(2) $\"+100+=+25t+\"$
\n" ); document.write( "(2) $\"+t+=+4+\"$
\n" ); document.write( " $\"+6+-+t+=+6+-+4+\"$
\n" ); document.write( " $\"+6+-+t+=+2+\"$
\n" ); document.write( "------------------
\n" ); document.write( "You spent 4 hrs on highway
\n" ); document.write( "You spent 2 hrs on back roads
\n" ); document.write( "---------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+d+=+70t+\"$
\n" ); document.write( "(1) $\"+d+=+70%2A4+\"$
\n" ); document.write( "(1) $\"+d+=+280+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+370+-+d+=+45%2A%28++6+-+t+%29+\"$
\n" ); document.write( "(2) $\"+370+-+d+=+45%2A2+\"$
\n" ); document.write( "(2) $\"+d+=+370+-+90+\"$
\n" ); document.write( "(2) $\"+d+=+280+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );