document.write( "Question 775609: If a boy walks from his house to school at 4 km/h, he reaches the school 10 minutes earlier than the scheduled time. However if he walks the rate of 3 km/h he reaches 10 minutes late. The distance of the school from his house is \n" ); document.write( "
Algebra.Com's Answer #473014 by josmiceli(19441)\"\" \"About 
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Let \"+t+\" = the time in hours for his trip
\n" ); document.write( "if he is to arrive at the scheduled time
\n" ); document.write( "Let \"+d+\" = distance from school to house in km
\n" ); document.write( "--------------
\n" ); document.write( "Equation for leaving early:
\n" ); document.write( "\"+d+=+4%2A%28+t++-+10%2F60+%29+\"
\n" ); document.write( "---------------------
\n" ); document.write( "Equation for leaving late:
\n" ); document.write( "\"+d+=+3%2A%28+t+%2B+10%2F60+%29+\"
\n" ); document.write( "---------------------
\n" ); document.write( "By substitution:
\n" ); document.write( "\"+4%2A%28+t+-+1%2F6+%29+=+3%2A%28+t+%2B+1%2F6+%29+\"
\n" ); document.write( "\"+4t+-+2%2F3+=+3t+%2B+1%2F2+\"
\n" ); document.write( "\"+t+=+1%2F2+%2B+2%2F3+\"
\n" ); document.write( "Multiply both sides by \"+6+\"
\n" ); document.write( "\"+6t+=+3+%2B+4+\"
\n" ); document.write( "\"+t+=+7%2F6+\"
\n" ); document.write( "-----------
\n" ); document.write( "By substitution:
\n" ); document.write( "\"+d+=+4%2A%28+70%2F60+-+10%2F60+%29+\"
\n" ); document.write( "\"+d+=+4+\" km
\n" ); document.write( "The distance of the school from his house is 4 km
\n" ); document.write( "------------
\n" ); document.write( "check:
\n" ); document.write( "\"+d+=+3%2A%28+t+%2B+10%2F60+%29+\"
\n" ); document.write( "\"+d+=+3%2A%28+t70%2F60%2B+10%2F60+%29+\"
\n" ); document.write( "\"+d+=+3%2A%284%2F3%29+\"
\n" ); document.write( "\"+d+=+4+\" km
\n" ); document.write( "OK
\n" ); document.write( "
\n" ); document.write( "
\n" );